Geometry Notes
7-5 Using Proportional Relationships
A scale drawing represents an object as smaller than or larger than its actual size.
The scale is the ratio of any length in the drawing to the corresponding actual length.
Ex. 1:
The scale in the map at
the right is (in meters):
1.5 cm
200 m
€
Find the distance
between the high
school and Phillips
Park.
1.5 cm 9.5 cm
=
200 m
x
1.5x = 1900
1900
x=
≈ 1267 m
1.5
€
Ex. 2: A rectangular house is 90 feet long by 50 feet wide. Make a scale drawing of the house,
using the scale 1 cm: 10 feet.
1 cm
x
=
10 ft 90 ft
10x = 90
x = 9 cm
€
1 cm
x
=
10 ft 50 ft
10x = 50
x = 5 cm
9 cm
5 cm
1
Ex. 3: On a Wisconsin road map, Kristin measured a distance of 11 in. from Madison to
8
Wausau. The scale of the map is 1 inch : 13 miles. To the nearest mile, what is the actual
distance between the two cities?
1 in 11.125
=
13 mi
x
x = 13(11.125) = 144.625
€
Distance : About 145 miles
€
Indirect measurement is any method using similar figures and proportions to measure an
object.
Ex. 4: Tyler wants to find the height of a telephone pole.
He measured the pole’s shadow and his own shadow and
then made a diagram. What is the height h of the pole?
5'9"= 5(12) + 9 = 69"
7'8"= 7(12) + 8 = 92"
38' 4"= 38(12) + 4 = 460"
69"
h
=
92" 460"
92h = 31740
31740
h=
= 345"
92
345 ÷12 = 28.75'
The pole is 28 ft 9 in tall.
€
Ex. 5: Find the area and perimeter of each rectangle below.
12
9
6
8
Perimeter: 9 + 6 + 9 + 6 = 30
Perimeter: 12 + 8 + 12 + 8 = 40
Area: 9(6) = 54
Area: 12(8) = 96
What is the similarity ratio of the dimensions of the rectangles?
What is the ratio of the perimeters of the rectangles?
9 3
=
12 4
30 3
=
40 4
€
54 9  32 
What is the ratio of the areas of the rectangles?
=
 2
€ 96 16  4 
Important Fact: Suppose the similarity ratio of two similar figures is
€
a
The ratio of their perimeters is .
b
a2
The ratio of their areas is 2 .
€ b
Ex. 6: ΔABC ~ ΔDEF. Find the perimeter and area of ΔABC.
€
Similarity ratio :
1 x
=
2 54
x = 27
6.5 1
=
13 2
12 1
x
= =
2
2
4 126
x = 31.5
Perimeter : 27 inches
€
Area : 31.5 in 2
.