Proportionality
and Measurement
FLORIDA
CHAPTER
5
Name
Class
Date
Lesson
Worktext
Copyright © by Holt McDougal. All rights reserved.
Remember It?
Student
Textbook
169 –170
Rev MA.6.A.2.1
Rev MA.6.A.2.2
5-1 Ratios and Proportions
202–205
Rev MA.6.A.2.1
Rev MA.6.A.2.2
5-2 Ratios, Rates, and Unit Rates
206 –209
Rev MA.7.A.1.1
5-3 Solving Proportions
210 –213
Rev MA.7.A.1.1
Rev MA.7.A.1.3
5-4 Similar Figures
216 –220
Rev MA.7.A.1.3
Rev MA.7.A.1.6
5-5 Scale Drawings and Scale
Models
221–224
MA.8.G.5.1
5-6 Dimensional Analysis
171–178
225 –229
MA.8.G.2.1
5-7 Indirect Measurement
179 –186
230 –233
Study It!
189
Write About It!
190
Chapter 5 Proportionality and Measurement 167
CHAPTER
Benchmark
5
Chapter at a Glance
Vocabulary Connections
LA.8.1.6.5 The student will relate new vocabulary to familiar words.
Key Vocabulary
Vocabulario
Vokabilè
conversion factor
factor de conversión
faktè konvèsyon
indirect measurement
medición indirecta
mezi endirèk
To become familiar with the vocabulary terms in the chapter, consider the following.
You may refer to the chapter, the glossary, or a dictionary if you like.
1. The word indirect means “not direct.” What do you think it means to find the length
of something using indirect measurement?
CHAPTER
2. The word convert means “to change from one form to another.” What do you think
would be the effect of using a conversion factor on a measurement or rate?
Copyright © by Holt McDougal. All rights reserved.
5
168 Chapter 5 Proportionality and Measurement
5-1
Name
Class
THROUGH
Date
5-5
Remember It?
Review skills and prepare for future lesson
lessons.
Lesson
5-1
Ratios and Proportions (Student Textbook pp. 202–205)
Rev MA.6.A.2.1,
Rev MA.6.A.2.2
4
Find
Fi
d ttwo ratios
ti that are equivalent to __
12 .
8
4 · 2 = __
_____
12 · 2
24
4÷2
______
= __26
12 ÷ 2
8:24 and 2:6 are equivalent to 4:12.
5
6
__
Simplify to tell whether __
15 and 24 form a proportion.
5÷5
6÷6
______
______
= __13
= __14
15 ÷ 5
24 ÷ 6
Since _1 ≠ _1 the ratios are not in proportion.
3
4
Find two ratios that are equivalent to each given ratio.
8
1. __
16
9
2. __
18
35
3. __
60
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Simplify to tell whether the ratios form a proportion.
8
4. __
and __26
24
3
6
5. __
and __
12
18
25
5
6. ___
and __
125
25
9
7. __68 and __
16
Lesson
5-2
Ratios, Rates, and Unit Rates
Rev MA.6.A.2.1,
Rev MA.6.A.2.2
(Student Textbook pp. 206–209)
Al can b
Alex
buy a 4 pack of AA batteries for $2.99 or an 8 pack for $4.98.
Which is the better buy?
price per package
$2.99
________________
= _____
≈ $0.75 per
4
number of batteries
battery
price per package
$4.98
________________
= _____
≈ $0.62 per
8
number of batteries
battery
The better buy is the 8 pack for $4.98.
Determine the better buy.
8. 50 blank CDs for $14.99 or 75 CDs for $21.50
9. 6 boxes of 3-inch incense sticks for $22.50 or 8 boxes for $30
10. 8 binders for $23.09 or 25 binders for $99.99
Lesson Tutorial Videos
Chapter 5 Proprotionality and Measurement 169
5-3
Lesson
Solving Proportions (Student Textbook pp. 210–213)
Rev MA.7.A.1.1
A car travels
l 14
145 mi in 2.5 h. At this rate, how far will the car go in
4 h?
x mi
145 mi = ____
______
4h
2.5 h
Set up a proportion.
580 = 2.5x
Find the cross products.
232 = x
The car will travel 232 miles in 4 hours.
Solve each proportion.
11. __35 = __9x
16
24 = __
12. __
4
h
11 = __
b
13. __
16
20
14. A kayaker traveled 2 miles in 40 minutes. At this rate, how long will
it take the kayaker to travel 9 miles?
Lesson
5-4
Similar Figures (Student Textbook pp. 216–220)
Rev MA.7.A.1.1,
Rev MA.7.A.1.3
A stamp 1
1.2
2 iinches tall and 1.75 inches wide is to be scaled to 4.2 inches tall.
How wide should the new stamp be?
1.2 = ___
4.2
____
x
1.75
Set up a proportion.
1.2x = 7.35
Find the cross products.
x = 6.125
The new stamp should be 6.125 inches wide.
15. A picture 3 in. wide by 5 in. tall is to be scaled to 7.5 in. wide
to be put on a flyer. How tall should the flyer picture be?
Lesson
5-5
Scale Drawings and Scale Models (Student Textbook pp. 221–224)
A llength
h on a map is 4.2 inches. The scale is 1 in:100 mi.
Find the actual distance.
1 in. = _____
4.2 in.
______
100 mi
x mi
1 · x = 100 · 4.2
x = 420 miles
Rev MA.7.A.1.3,
Rev MA.7.A.1.6
scale length
Set up a proportion using ___________.
actual length
Find the cross products.
The actual distance is 420 miles.
17. A length on a scale drawing is 5.4 cm. The scale is 1 cm:12 m. Find
the actual length
The scale of a map is 1 in.:10 mi. How many actual miles does each
measurement represent?
18. 4.6 in.
19. 5__34 in.
20. 15.3 in.
170 Chapter 5 Proprotionality and Measurement
21. 7__14 in.
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16. A picture 8 in. wide by 10 in. tall is to be scaled to 2.5 in. wide to be
put on an invitation. How tall should the invitation picture be?
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5-6
Date
MA.8.G.5.1 Compare, contrast, and
convert units of measure between
different measurement systems
(US customary or metric (SI)) and dimensions
including…derived units to solve problems.
Dimensional Analysis
Convert Between Measurement Systems
By making and comparing measurements in different
systems of measurement, you can determine the
factors you can use to convert between the two
systems.
Activity 1
Answers are approximate.
___
1 Measure the length of AB in inches and in centimeters.
A
B
length (in.)
length (cm)
2 Divide the measurements to find the conversion factors. Give factors to the
nearest hundredth.
length (cm)
length (in.)
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1 in. = __________ =
cm
length (in.)
length (cm)
1 cm = __________ =
in.
3 A bookshelf is 14 inches wide. Find
the length in centimeters to the nearest
tenth.
14 in. × (
cm per in.) =
cm
A sheet of paper is 24 centimeters
long. Find the length in inches to the
nearest tenth.
24 cm × (
in. per cm) =
in.
Try This
Convert between inches and centimeters. Give answers to the nearest tenth.
1. 10 in.
2. 4 in.
3. 36 in.
4. 22.8 in.
5. 5 cm
6. 60 cm
7. 100 cm
8. 15.5 cm
Draw Conclusions
9. Explain whether the conversion factors that you found in Step 2 are exact or
approximate.
5-6 Dimensional Analysis 171
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In Activity 1, you converted a measurement from one unit to another. Sometimes
you may have to convert multiple units. One way to do that is to carry out the
conversions one at a time.
Activity 2
A car is traveling 60 miles per hour. How fast is it traveling in inches per second?
To solve, first convert miles to inches. Then convert hours to seconds.
Use conversion factors that you know.
1 miles
to inches
−−−−−−−−−
1 mi = 5280 ft
So, 60 mi = 60 × 5280 =
1 ft = 12 in.
So,
ft
ft =
× 12 =
in.
2 hours
to seconds
−−−−−−−−−−−
1 h = 60 min and 1 min = 60 s
So 1 h = 60 × 60 =
s
3 Use your answers to Steps 1-2. Remember that per means “divide by.”
60 mi = ______________
in. =
60 miles per hour = _____
1h
inches per second
s
4 Steps 1-3 can be expressed in a single equation. To do this, set up conversion
factors so that the answer is in the desired units only, and any units not in the
answer will cancel out.
The car is traveling 1056 inches per second.
Try This
Convert.
10. 30 mi/h to ft/s
11. 12 ft/min to yd/h
12. 40 gal/day to qt/week
13. 50 m/min to cm/h
Draw Conclusions
14. Explain how you could use the results from Activities 1 and 2 to convert
10 in./s to cm/min.
172 5-6 Dimensional Analysis
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5280 ft
12 in. × ______
1 h × _____
1 min
60 mi × ______
_____
× _____
60 s
1 mi
60 min
1h
1 ft
60
× 5280 × 12 in.
1056
in.
_______________
_______
= 1 × 60 × 60 s = 1 s
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5-6
Date
MA.8.G.5.1 Compare, contrast, and
convert units of measure between
different measurement systems
(US customary or metric (SI)) and dimensions
including…derived units to solve problems.
Learn It!
Dimensional Analysis (Student Textbook pp. 225
225–229)
Lesson Objective
Use one or more conversion factors to solve problems.
Vocabulary
conversion factor
Example 1
Convert each measure.
A. 63 feet to yards
yd
63 feet · ________
yd
Multiply by the conversion factor ________ .
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ft
ft
1 yd
63 ft · ____
____
1
3 ft
Divide out
63 yd
_____
=
3
yd
. Then multiply.
Divide.
yards.
63 feet is equal to
B. 5.2 meters to centimeters
cm
5.2 m · _________
cm .
Multiply by the conversion factor _________
m
m
100 cm
5.2 m · ______
_____
1
1m
520 cm =
______
1
Divide out
cm
5.2 meters is equal to
. Then multiply.
Divide.
centimeters.
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5-6 Dimensional Analysis 173
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1a. Convert 8 pounds to ounces.
Example 2
1b. Convert 0.2 liters to milliliters.
Problem Solving Application
A car traveled 60 miles on a road in 2 hours. How many feet per second
did the car travel?
1
Understand the Problem
The answer is in units of feet and seconds. The problem is stated in units of miles
and hours. You will need to use several conversion factors. List the important
information:
1 mile =
feet
1 hour =
minutes
1 minute =
seconds
Make a Plan
Multiply by each
factor separately, or simplify the
problem and multiply by several
factors at once.
Set up conversion factors so that the answer is in the desired units only, and any
units not in the answer will cancel out.
ft · __
mi · ___
h = ______
___
h mi s
3
Solve
First, you can convert 60 miles in 2 hours into a unit rate.
÷ 2) mi
60 mi = (60
mi
_____
_________
= _________
2h
(2 ÷ 2) h
h
5280 ft · _____
30 mi · ______
1h
_____
1 mi 3600s
1h
Set up the
174 5-6 Dimensional Analysis
factors.
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2
seconds, so 1 hour =
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158,400 ft
· 5280 ft · 1
30
___________
= ________
= _______ft
1 · 1 · 3600
3600 s
Practice It!
Apply It!
Multiply.
s
The car traveled
4
feet per second.
Look Back
60 miles in 2 hours is 30 mi/h. 1 mi/h is 5280 feet in 3600 seconds, or about
1_12 ft/s, so 30 miles per hour is about 1_12(30) ≈ 45 ft/s, which is close to the answer.
Check It Out!
2. Bijou drives her car 23,000 miles per year. Find the number of miles she drives
per month.
Example 3
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O
Owen
is
i 6 feet
f
tall. To the nearest whole number, what is his height in
centimeters?
cm
12 in · ________
6 ft · ____
1 in.
Multiply by conversion factors.
6 ft · ____
cm
12 in · _________
___
1
1 in.
1 ft
Divide out common units. Then multiply.
1 ft
cm
____________
≈
1
Owen is about
cm
Divide.
centimeters tall.
Check It Out!
3. How many kilometers is 26 miles?
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5-6 Dimensional Analysis 175
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Date
MA.8.G.5.1 Compare, contrast, and
convert units of measure between
different measurement systems
(US customary or metric (SI)) and dimensions
including…derived units to solve problems.
Summarize It!
Dimensional Analysis
Think and Discuss
lb
lb
___
1. Give the conversion factor for converting __
yr to mo .
2. Explain how to find whether 10 mi/h is faster than 15 ft/s.
3. Get Organized Complete the graphic organizer. Fill in the blanks to show the
sequence of steps for converting 6.2 kilograms to pounds and back again.
conversion
factor
show your
work
START
ending
quantity
first
result
show your
work
END
176 5-6 Dimensional Analysis
conversion
factor
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initial
quantity
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5-6
Date
MA.8.G.5.1 Compare, contrast, and
convert units of measure between
different measurement systems
(US customary or metric (SI)) and dimensions
including…derived units to solve problems.
Dimensional Analysis
Find the appropriate factor or factors for each conversion.
1. millimeters to meters
2. inches to yards
3. days to minutes
4. kilograms to grams
5. miles to kilometers
6. liters to quarts
7. Convert 1300 pounds to tons. Show your work.
8. Marci drinks four 48-ounce glasses of water a day.
How many pints of water does she drink every day?
9. Mari bought 9_12 yards of ribbon. How many inches
of ribbon did she buy?
10. A bag of frozen vegetables weighs 42 ounces. How many
pounds does the package of vegetables weigh?
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11. The 18th hole on the local golf course is 543 yards long.
How many feet is this distance?
Find the resulting unit.
price __
oz
13. _____
oz · lb
m
12. cm · ___
cm
g
kg
· __
14. kg · __
kg g
cm __
m · ___
·h
15. __
h m s
Convert. Round to the nearest tenth.
16. 85 km/h to mi/h
17. 15 gal/min to qt/s
18. 10 cm/s to ft/min
19. 32 ft/s to mi/h
20. A commercial airplane has a takeoff speed of
about 300 km/h. What is the takeoff speed in mi/h?
21. A french-fry machine is able to process 30 pounds of potatoes in
one minute. Express the machine’s rate in kilograms per hour.
22. A hydroelectric dam lets water through at a rate of 1000 gal/min.
What is the rate in liters per second?
5-6 Dimensional Analysis 177
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MA.8.G.5.1 Compare, contrast, and
convert units of measure between
different measurement systems
(US customary or metric (SI)) and dimensions
including…derived units to solve problems.
Apply It!
Dimensional Analysis
1. The price of a meteorite is $25 per gram.
One gram is about 0.0353 ounces. Yuri
wants to buy a 2.5 ounce meteorite. How
much will it cost to the nearest dollar?
5. A doctor needs to administer a dosage
of 0.12 mg of epinephrine to a patient. A
bottle contains 1 mL epinephrine per 1000
mL solution, and 1 mg = 1 mL. How much
solution should be used?
2. Kait and Tom replaced their old cars. Kait’s
gas mileage improved from 10 mi/gal to
12.5 mi/gal, Tom’s improved from 25 mi/gal
to 40 mi/gal. At $4 a gallon, who saved more
money per 1000 miles? How much?
The distances from Pensacola, FL to several
Florida cities and towns are shown. 1 mile is
about 1.61 km. Use the table for 5–7.
City or Town
Boynton Beach
Key Largo
Bottles
Price
8 ounce
36
$5.75
20 ounce
24
$6.50
1
_
liter
2
35
$6.25
700 mL
24
$6.75
1L
15
$5.99
Price/oz
3. Complete the table. Round each price to the
nearest tenth of a cent.
4. Which size is the best buy?
178 5-6 Dimensional Analysis
1113
644
Okeechobee
861
1006
6. At a speed of 55 miles per hour, which
location would take about 9 hours and 45
minutes to reach from Pensacola? Justify
your answer.
7. Gridded Response
At what speed, in miles
per hour, would it take
12 hours to reach Key
Largo from Pensacola?
Round to the nearest
whole number.
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Size
965
New Port Richey
Weston
The table shows the prices of several cases of
bottled water. 1 liter is about 33.8 ounces. Use
the table for 3–4.
Distance from
Pensacola (km)
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Date
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MA.8.G.2.1 Use similar triangles to
solve problems that include height and
distances.
Indirect Measurement
Use Similar Figures
In similar figures, the ratio of the lengths of two sides of one figure is equal to the ratio
of the lengths of the corresponding sides of the other figure. Similar figures have the
same shape. They do not always have the same size.
Activity 1
If the day is sunny, you can use shadows to find unknown dimensions in
similar figures. The shows the measurements you will be making in Steps 1–3.
1
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3
2
1 With a classmate, measure your height.
height =
2 Go outside together and measure the length
of your shadow.
length of your shadow =
3 While still outside, measure the length of
the shadow of a tall object such as a flagpole
or your school building.
4 Write the name of the tall object whose
shadow you measured.
object measured:
5 Find the ratio of your height to the length of
your shadow.
ratio =
length of tall
object’s shadow =
6 Multiply the ratio from Step 5 by the length of the tall object’s shadow.
The product is the actual height of the tall object.
ratio × tall object’s shadow length =
×
actual height of tall object =
5-7 Indirect Measurement 179
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Try This
Use what you discovered in the activity to find the height of the flagpole.
1.
2.
5 ft
156 ft
78 in.
12 ft
450 in.
flagpole height =
195 in.
flagpole height =
3.
4.
1.5 m
88 m
flagpole height =
5.5 ft
4m
105 ft
27.5 ft
flagpole height =
Draw Conclusions
5. How could the technique in this activity be useful in real life?
6. Suppose you knew the height of the flagpole but could not measure its shadow
length directly. Could you use indirect measurement to measure it? Explain.
S
V
M
180 5-7 Indirect Measurement
N
Q
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7. If you knew SQ, MN, and NQ, how could you find VN?
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MA.8.G.2.1 Use similar triangles to
solve problems that include height and
distances.
Indirect Measurement (Student Textbook pp. 230–233)
Lesson Objective
Find measures indirectly by applying the properties of similar figures
Vocabulary
indirect measurement
Example 1
Triangles
T
i
l AB
ABC and EFG are similar. Find the distance EG.
F
B
3 ft
A
9 ft
C
4 ft
G
x ft
and
Triangles
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E
are similar. Set up a proportion.
EG = _____
AC
___
EF
Substitute
for AC,
for EF, and
for AB.
4
x = _____
_____
=
3x = _____
36
_____
Find the
Divide both sides by
.
.
x=
The distance EG is
feet.
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5-7 Indirect Measurement 181
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1. The triangles are similar. Find the distance across the river.
xm
3m
9m
4m
Example 2
Problem Solving Application
A 30-ft building casts a shadow that is 75 ft long. A nearby tree casts a
shadow that is 35 ft long. How tall is the tree?
1
Understand the Problem
The answer is the
of the tree in units of
.
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List the important information:
• The height of the building is
ft.
• The length of the building’s shadow is
ft.
• The length of the tree’s shadow is
2
ft.
Make a Plan
Use the information to
.
30 ft
h
75 ft
182 5-7 Indirect Measurement
35 ft
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3
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Solve
Draw a diagram. Then draw the dashed lines to form triangles. The building
triangles.
and its shadow and the tree and its shadow form similar
h = _____
_____
Corresponding sides of similar figures are
.
=
75h
1050
_____
= _____
Find the
.
Divide both sides by
.
h=
The height of the tree is approximately
4
ft.
Look Back
4
4
Since _____ = __
, the building’s shadow is __
of its height. So, the tree’s
10
10
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4
4
shadow should also be __
of its height and __
of
10
10
is approximately 6.
Check It Out!
2. A 5-ft tall student casts a shadow that is 7 ft long. A nearby light pole casts a
shadow that is 21 ft long. How tall is the light pole?
x ft
5 ft
21 ft
7 ft
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5-7 Indirect Measurement 183
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Date
MA.8.G.2.1 Use similar triangles to
solve problems that include height and
distances.
Indirect Measurement
Think and Discuss
1. Describe a situation for which it would make sense to use indirect
measurement to find the height of an object.
2. Explain how you can tell whether the terms of a proportion you have written
are in the correct order.
3. Get Organized A tower of height x feet has a shadow of length 90 feet at the
same time that a person of height 6 feet has a shadow of length 15 feet. Find
the height of the tower, then fill in the graphic organizer to show whether the
proportion is true.
tower's height ? tower's shadow
=
person's shadow
person's height
Indirect
Measurement
? person's shadow
tower's shadow =
person's height
tower's height
184 5-7 Indirect Measurement
? tower's height
tower's shadow =
person's shadow person's height
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tower's height ? person's height
=
tower's shadow person's shadow
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MA.8.G.2.1 Use similar triangles to
solve problems that include height and
distances.
Indirect Measurement
1. Find the height of the building.
2. Find the length of the lamppost’s shadow.
h
10 ft
6 ft
4 ft
7.5 ft
39 ft
12 ft
3. A building casts a shadow that is 420 meters long. At the same time,
a person who is 2 meters tall casts a shadow that is 24 meters long.
How tall is the building?
4. On a sunny day around noon, a tree casts a shadow that is 12 feet
long. At the same time, a person who is 6 feet tall standing beside
the tree casts a shadow that is 2 feet long. How tall is the tree?
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5. How wide is the lake?
6. How wide is the river?
d yd
wm
60 yd
3 yd
15yd
5m
3 m 15 m
7. The lower cable meets the tree at a height of 6
feet and extends out 16 feet from the base of the
tree. The triangles are similar.
a. How tall is the tree?
b. How long is the upper cable
to the nearest tenth of a foot?
56 ft
5-7 Indirect Measurement 185
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Date
MA.8.G.2.1 Use similar triangles to
solve problems that include height and
distances.
Indirect Measurement
1. Can an 80-foot-long cable cross the width of
the canyon? Explain.
?
Jamie measured the shadow length of a 1.5 m
stick at 4 different times. Use this information
and the table for 4-5.
Measurement
25 ft
5 ft
17 ft
2. Celine estimates that she can swim across
the pond at about _34 m/s. How far will she
swim in meters? How long will it take her in
minutes?
Shadow length
(cm)
Measurement 1
85
Measurement 2
160
Measurement 3
275
Measurement 4
380
4. Jamie’s shadow length was 285 cm
at the same time he made one of the
measurements in the table. How tall
must Jamie be in meters to the nearest
hundredth? Explain.
?
54 m
12 m
3. Paula places a mirror at point C so she can
see the top of the flagpole in the mirror. Her
eye height is 5 feet and she stands 6 feet
from the mirror. The mirror is 25 feet from
the flagpole. How tall is the flagpole to the
nearest foot?.
B
D
A
C
186 5-7 Indirect Measurement
E
5. How long was Jamie’s shadow to the nearest
tenth of a foot when his shadow length was
shortest?
6. Gridded Response
The WDJR-FM Radio
Tower in Bethlehem,
FL, is 1901 feet tall.
D’Asia is 5 feet tall.
When the tower’s
shadow is 1.5
kilometers long, how
long is D’Asia’s shadow
to the nearest foot?
Copyright © by Holt McDougal. All rights reserved.
50 m
5-6
Name
Class
THROUGH
Date
5-7
Got It?
Ready to Go On?
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Quiz for Lessons 5-6 through 5-7
5-6
Dimensional Analysis (Student Textbook pp. 225–229)
Convert each measure.
1. 128 fluid ounces to cups
2. 420 centimeters to meters
3. 20 quarts to gallons
4. 1.5 miles to feet
5. 14.2 meters to centimeters
6. 480 milligrams to grams
7. Driving at a constant rate, Shawna covered 325 miles in 6.5 hours.
Express her driving rate in feet per minute.
8. A recipe from a British cookbook calls for 150 milliliters of milk.
There are about 237 milliliters in 1 cup. To the nearest whole
number, how many fluid ounces of milk are needed for the recipe?
9. A three-toed sloth has a top speed of 0.22 feet per second. A giant tortoise
has a top speed of 2.992 inches per second. Convert both speeds to miles per
hour, and determine which animal is faster.
Copyright © by Holt McDougal. All rights reserved.
5-7
Indirect Measurement (Student Textbook pp. 230–233)
10. At the same time that a flagpole casts a 4.5 meter shadow, a meter
stick casts a 1.5 meter shadow. How tall is the flagpole?
11. A tree casts a 30 foot shadow. Mi-Ling, standing next to the tree,
casts a 13.5 foot shadow. If Mi-Ling is 5 feet tall, how tall is the tree?
12. A person whose eyes are at a height of 5 feet sets up a
mirror to see a treetop, forming similar triangles. The
person is 2 feet from the mirror and the tree is 13 feet
from the mirror. How tall is the tree?
13. Kayla draws the two triangles shown and
determines that the height of the column is
42.875 meters. Explain whether
Kayla is correct
2m
24.5 m
3.5 m
Chapter 5 Proportionality and Measurement 187
5-6
THROUGH
5-7
Name
Class
Connect It!
Date
MA.8.G.2.1, MA.8.G.5.1
Connect the Concepts of Lessons 5-6 through 5-7
Up, Up, and Away!
The Miami SkyLift is a helium balloon that carries 30 passengers
into the air for an incredible view of the Miami area.
1. The balloon is attached to the ground by a cable. When the
balloon is at its maximum height, the shadow of the balloon
and cable is 30.5 m long. A nearby flagpole that is 6 m tall
casts a shadow that is 1.2 m long. What is the maximum
height of the balloon?
6m
30.5 m
1.2 m
2. What is the maximum height to the nearest foot?
3. The SkyLift ride lasts 15 minutes. Suppose one-third of that
time is spent rising to the maximum height. At what rate does
the balloon rise?
4. A passenger claims that the balloon rises at about 20 mi/h. Do you
agree or disagree? Explain.
1. Find the greater measurement on each
ticket. Circle the letter of the greater
measurement.
7100 mm
2400 g
90 cm
R
S
E
53 m
0.8 kg
50 in.
O
C
N
14 lb
45 mi/h
20 m/s
B
T
L
6 kg
61 ft/s
75 km/h
A
M
O
2. Arrange the circled letters to spell the
name of the city where the first World
Series game was played, in 1903.
188 Chapter 5 Proportionality and Measurement
Copyright © by Holt McDougal. All rights reserved.
Tickets to the World Series
FLORIDA
Name
Class
Study It!
Vocabulary
5
Multi-Language
Glossary
Go to thinkcentral.com
(Student Textbook page references)
conversion factor . . . . . . . (225)
Lesson 5-6
CHAPTER
Date
indirect measurement. . . (230)
Dimensional Analysis (Student Textbook pp. 225–229)
D
MA.8.G.5.1
At a rate of 75 kilometers per hour, how many meters does a car travel in 1 minute?
75 km · ______
1000 m · ______
1250 m
1 h = ______
_____
60 min
1 min
1h
1 km
The car travels 1250 meters in 1 minute.
Convert each measure.
1. 12.5 m to cm
2. 0.5 mi to ft
3. 35 mm to cm
4. 10.5 ft to yd
5. 27 in to cm
6. 18 mi to kilometers
7. If $1 is 0.67 euro, a car gets 25 miles to the gallon, and a gallon of gas
costs $3.75, how much does it cost to the nearest euro to go 500 miles?
Copyright © by Holt McDougal. All rights reserved.
8. A tank can go 55 feet on 4 ounces of gasoline. How many miles per
gallon does the tank get?
Lesson 5-7
IIndirect Measurement (Student Textbook pp. 230–233)
MA.8.G.2.1
A telephone pole costs a 5 ft shadow at the same time that a man next to it casts
a 1.5 ft shadow. If the man is 6 ft tall, how tall is the pole?
1.5
___
= __6x
5
Set up a proportion.
Find the cross products
1.5x = 30
x = 20
The telephone pole is 20 ft tall.
9. What is the distance d across the ravine?
6 ft
d
10 ft
21 ft
Ravine
10. A flagpole casts a 15 ft shadow at the same time that
Jon casts a 5 ft shadow. If Jon is 6 ft tall, how tall is the flagpole?
Chapter 5 Proportionality and Measurement 189
Name
Class
Write About It!
Date
LA.8.2.2.3 The student will organize
information to show understanding
or relationships among facts, ideas…
(e.g., representing key points within text
through…summarizing…)
Think and Discuss
Answer these questions to summarize the important concepts from Chapter 5
in your own words.
1. Explain how to convert from a smaller unit, such as inches, to a larger unit, such
as feet.
2. Explain how to convert from a larger unit to a smaller unit.
3. Show how you can convert back to the original units after a conversion.
5. Explain how to find the distance across the river d if
you know distances a, b, and c.
d
a
b
Before The Test
I need answers to these questions:
190 Chapter 5 Proportionality and Measurement
c
Copyright © by Holt McDougal. All rights reserved.
4. The height of an object cannot be measured directly. How can you use shadows
to measure the object?