Page 1 of 6
Proportions and Scale Drawings
BEFORE
Now
WHY?
You used mental math to find
the actual length of an object.
You’ll use proportions to find
measures of objects.
So you can find the height of the
Statue of Liberty in Ex. 3.
In the Real World
Word Watch
Review Words
scale drawing, p. 68
scale, p. 68
Soap Box Derby You are building a car for a Soap Box Derby race. In
the scale drawing of the Derby car shown below, the car has a length of
2.8 inches. What is the actual length of the Derby car?
length: 2.8 in.
width: 0.6 in.
1 in. : 2.5 ft
The scale of 1 in. : 2.5 ft on the drawing is a ratio that means 1 inch on the
drawing represents an actual distance of 2.5 feet on the car.
1 in.
2.5 ft
EXAMPLE
1
Measure on drawing
Actual measure
Using a Scale Drawing
To find the actual length of the car above, write and solve a proportion.
Let x represent the Derby car’s actual length in feet.
Length on drawing
1 in.
2.5 ft
Actual length
Write a proportion.
1 in.
2.8 in.
2.5 ft
x ft
Substitute values.
1 p x (2.5)(2.8)
The cross products are equal.
x7
Multiply.
ANSWER The actual length of the Derby car is 7 feet.
Your turn now
Use the scale drawing shown above.
1. Find the actual width of the Derby car.
2. If the actual wheelbase of the Derby car is 5.5 feet, what is the
wheelbase of the car in the scale drawing?
388
Chapter 8
Ratio, Proportion, and Percent
Page 2 of 6
Perimeter and Area The ratio of the perimeter of a scale drawing to
the actual perimeter is related to the scale. So is the ratio of the areas.
EXAMPLE
with
Review
Need help with finding the
perimeter and area of a
rectangle? See p. 61.
2
Finding Ratios of Perimeters
School Murals A finished mural is to be 20 feet by 10 feet. Your scale
drawing of the mural is shown below.
2 in.
a. What is the perimeter of the
drawing? of the mural?
b. Find the ratio of the drawing’s
perimeter to the mural’s
perimeter. How is this ratio
related to the scale?
1 in.
1 in. : 10 f t
Solution
a. Perimeter of drawing: P 2l 2w 2(2) 2(1) 6 in.
Perimeter of mural:
Perimeter of drawing
P 2l 2w 2(20) 2(10) 60 ft
6 in.
1 in.
b. 60 ft
10 ft
Perimeter of mural
ANSWER The ratio of the perimeters is the same as the scale.
EXAMPLE
3
Finding Ratios of Areas
Use the information from Example 2. Find the ratio of the drawing’s area
to the mural’s area. How is this ratio related to the scale?
Solution
Area of drawing:
A lw 2 p 1 2 in.2
Area of mural:
A lw 20 p 10 200 ft2
Area of drawing
2 in.2
1 in.2
1 p 1 in.2
2 2 2
Area of mural
200 ft
100 ft
10 p 10 ft
ANSWER The ratio of the areas, 12 in.2: 102 ft2, is the square of the scale.
Your turn now
A scale drawing of another mural has a length of 5 cm
and a width of 3 cm. The scale of the drawing is 1 cm : 2 m.
3. What is the ratio of the perimeters of the drawing and the mural?
4. What is the ratio of the areas of the drawing and the mural?
Lesson 8.4
Proportions and Scale Drawings
389
Page 3 of 6
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 715
Getting Ready to Practice
1. Vocabulary Express the scale 1 in. : 5 ft as a ratio in two other ways.
2. A scale drawing has a scale of 1 in. : 6 ft. The actual length of the object
is 48 feet. Choose the proportion you can use to find the length of the
drawing. Then find the length.
Length of drawing
1 in.
B. 6 ft
48 ft
1 in.
48 ft
A. 6 ft
Length of drawing
3. Statue of Liberty The model shown has a scale
of about 1 in. : 20 ft. Copy and complete the
proportion below to find the combined
height of the actual Statue of Liberty
and the pedestal.
15 in.
Height of model
1 in.
20 ft
Height of actual monument
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
4–9
10–16
10–16
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
A scale drawing of a very small object is larger than the object. The
scale of a drawing is 2 cm : 9 mm. Find the unknown measure.
4. length on drawing 6 cm;
length of object _?_
5. width of object 45 mm;
width on drawing _?_
A map uses a scale of 1 in. : 50 mi. Find the actual distance for
the given distance on the map.
6. 3 inches
7. 8 inches
8. 0.5 inch
9. 4.5 inches
Geometry In Exercises 10–13, use the table.
10. Choose one of the rectangles.
Use a metric ruler to draw the rectangle.
11. Describe Enlarge your rectangle so
that 2 centimeters on the new rectangle
represents 1 centimeter on the original
rectangle. Describe your method.
Rectangle 1
4 cm 2 cm
Rectangle 2
3 cm 5 cm
Rectangle 3
6 cm 6 cm
12. Find the perimeters and areas of the original and enlarged rectangles.
13. Interpret Write the ratio of the perimeters and the ratio of the areas.
Explain how these ratios are related to the scale.
390
Chapter 8
Ratio, Proportion, and Percent
Page 4 of 6
Landscape Architects A landscape architect is designing a garden
for a city park. The drawing has a scale of 1 cm : 5 m. Use the
drawing in Exercises 14–16.
14. Find the actual dimensions
of the garden.
15. Find the ratio of the
drawing’s perimeter to
the garden’s perimeter.
16. Find the ratio of the
drawing’s area to
the garden’s area.
17. Critical Thinking Are there 12 square inches in 1 square foot? Are there
3 square feet in 1 square yard? Why or why not? Explain.
18. Challenge If a scale drawing has the scale a : b, write algebraic
expressions for the ratio of the perimeters and for the ratio of the areas.
Mixed Review
19. Choose an appropriate customary unit to measure the weight of a
dining table. (Lesson 7.6)
Solve the proportion. (Lesson 8.3)
x
5
20. 16
4
2
22
21. 3
a
9
6
22. 21
y
10
25
23. n
40
Basic Skills Use mental math to find the quotient.
24. 1.5 10
25. 71 10
26. 230 100
27. 68 100
Test-Taking Practice
CLASSZONE.COM
28. Multiple Choice Based on the scale
Clinton
provided, what is the actual direct
distance from Hamilton to Clinton?
A. 2 km
B. 15 km
C. 17 km
D. 30 km
m
State Test Practice
2c
INTERNET
Hamilton
1 cm : 15 km
29. Multiple Choice A model airplane uses the scale 2 in. : 15 ft. The
model’s length is 20 inches. What is the actual length of the airplane?
F. 30 in.
G. 100 in.
Lesson 8.4
H. 150 ft
I. 400 ft
Proportions and Scale Drawings
391
Page 5 of 6
8.1TO
8. 4
Notebook Review
Check Your Definitions
scale drawing, p. 68
scale, p. 68
ratio, p. 374
Review the
vocabulary
definitions in
your notebook.
Copy the review
examples in your
notebook. Then
complete the
exercises.
equivalent ratio, p. 375
rate, p. 379
unit rate, p. 379
proportion, p. 383
cross products, p. 383
Use Your Vocabulary
1. Copy and complete: A _?_ is a ratio of two measures that have different
units.
2. Copy and complete: A proportion is an equation you write to show that
two _?_ are _?_.
2
4
3. What are the cross products for the proportion ?
x
6
8.1–8.3 Can you use ratios, rates, and proportions?
EXAMPLE Solve the proportion.
3
x
a. 4 1
2
10
x
b. 4 14
Use equivalent ratios.
33
You multiplied 4
x
3
by 3 to get 12,
12
4
so multiply 3 by
3 also.
43
Use cross products
and a related equation.
3 3 9, so x 9.
140 4 x
x
10
14
4
140 4x
35 x
✓
20 in.
100 in.
4. Copy and complete to write an equivalent rate: .
9 sec
?
7
5. Copy the statement: 8 out of 12 _?_ . Then write the ratios as
9
decimals and use <, >, or to complete the statement.
6. Four pounds of tomatoes cost $10. Find the unit price.
x
18
7. Solve the proportion .
4
6
392
Chapter 8
Ratio, Proportion, and Percent
Page 6 of 6
8.4 Can you find measurements with scale drawings?
EXAMPLE A map uses a scale of 1 in. : 75 mi. On the map, two cities
are 2 inches apart. What is the actual distance between the cities?
Distance on map
1 in.
75 mi
Actual distance
Write a proportion.
1 in.
2 in.
75 m i
x mi
Substitute values.
1 p x 75 p 2
The cross products are equal.
x 150
Multiply.
ANSWER The actual distance between the cities is 150 miles.
✓
8. A model uses the scale 2 in. : 5 ft. The length of the model is
50 inches. What is the actual length?
about Lessons 8.18.4
9. Writing Compare a rate with a unit rate. How are they alike? How are
they different? Explain.
Review Quiz 1
Match the ratio with an equivalent ratio.
1. 5 to 30
2. 12 : 4
A. 3 to 1
B. 6
1
3. 24 to 18
4. 9 : 72
C. 1 : 8
D. 4 to 3
5. Shopping A 32 ounce carton of juice costs $3.20. A 16 ounce carton of
juice costs $1.92. Which carton is the better buy? Explain.
Solve the proportion.
4
x
6. 21
84
25
100
7. z
84
8
36
8. 10
g
n
8
9. 30
12
10. Geometry Use a metric ruler to make a
scale drawing of the rectangle shown
using the scale 1 cm : 5 cm. Then find
the ratio of the area of the original
rectangle to the area of the enlarged rectangle.
Lessons 8.1–8.4
1 cm
2 cm
Notebook Review
393