1. Learn to understand ratios and proportions in scale drawings
Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.

2. Vocabulary
scale drawing
scale factor
scale model
scale

3. A scale drawing is a proportional two-dimensional drawing of an object.
Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. For example, if a drawing of a building has
a scale factor of , this means that each
dimension of the drawing is of the
corresponding dimension of the actual building. 1 87 1 87

4. A scale model is a proportional three- dimensional model of an object.
A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train.

5. Additional Example 1: Finding a Scale Factor
Identify the scale factor.
13.5
108
Width (in.)‏ 18
144
Length (in.)‏
Blueprint
Room
blueprint length
room length 18
144
Write a ratio using one of the
dimensions. = 1 8 =
Simplify.
A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions.
Caution! 1 8
The scale factor is .

6. Check It Out: Example 1
Identify the scale factor. 3 18
Wing span (in.)‏ 2 12
Length (in.)‏
Blueprint
Model Aircraft
blueprint length
aircraft length 2 12 =
Write a ratio using one of the dimensions. 1 6 =
Simplify.
The scale factor is . This is reasonable because of the length of the model is 3 in. The length of the blueprint is 2, which is less. is less than . 1 6 4

7. Additional Example 2: Using Scale Factors to Find Unknown Lengths
A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches.
The scale factor is . Find the size of the photograph. 5 1
poster
photo 5 1
Think: = 36 l 5 1 =
Write a proportion to find the length l.
5l = 36
Find the cross products.
l = 7.2
Divide.

8. Additional Example 2 Continued
A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches.
The scale factor is . Find the size of the photograph. 5 1
poster
photo 5 1
Think: =
20.5 w 5 1
Write a proportion to find the width w. =
5w = 20.5
Find the cross products.
w = 4.1
Divide.
The photo is 7.2 in. long and 4.1 in. wide.

9. Additional Example 3: Measurement Application
On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles?
Let d be the actual distance between the cities.
1.5 60
7.5(in)
D (mi) =
Write a proportion.
1.5 · d = 60 · 7.5
Find the cross products.
1.5d = 450
Multiply.
1.5d
1.5
450
1.5 =
Divide both sides by 1.5.
d = 300
The distance between the cities is 300 miles.