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5-7 Scale Drawings and Scale Models
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm UpWrite each fraction in the simplest form.
Course 2
5-7 Scale Drawings and Scale Models
1. 4
482. 9
135
Convert the following measurements.
3. 192 inches = feet
4. 18.5 feet = inches
5. 324 inches = feet
16
222
27
112
115
Problem of the Day
A toy model of a 200 foot dinosaur is 3 in. long. How many times as long as the model is the dinosaur? 800 times as long
Course 2
5-7 Scale Drawings and Scale Models
Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.
Course 2
5-7 Scale Drawings and Scale Models
Vocabulary
scale modelscale factorscalescale drawing
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Course 2
5-7 Scale Drawings and Scale Models
Course 2
5-7 Scale Models and Scale Drawings
This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO
gauge model train is . 1
87
This means that each dimension of the model is of the corresponding dimension of the actual train.
187
Course 2
5-7 Scale Models and Scale Drawings
A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph showsa scale drawing of the model train.
A scale drawing is a proportional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.
Identify the scale factor.
Additional Example 1: Finding a Scale Factor
Course 2
5-7 Scale Drawings and Scale Models
Room Blueprint
Length (in.) 144 18
Width (in.) 108 13.5
blueprint lengthroom length
= 1818
The scale factor is .
Write a ratio using one of thedimensions.
Simplify.
18144
=
Try This: Example 1
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Course 2
5-7 Scale Drawings and Scale Models
Identify the scale factor.
Model Aircraft Blueprint
Length (in.) 12 2
Wing span (in.) 18 3
blueprint length aircraft length
= 212
= 16
The scale factor is .16
Write a ratio using one of the dimensions.
Simplify.
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.
Additional Example 2: Using Scale Factors to Find Unknown Lengths
Course 2
5-7 Scale Drawings and Scale Models
51
Think: posterphoto
= 51
36 l
= 51
5l = 36
l = 7.2
Write a proportion to find the length l.
Find the cross products.
Divide.
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.
Additional Example 2 Continued
Course 2
5-7 Scale Drawings and Scale Models
51
Think: posterphoto
= 51
20.5 w
= 51
5w = 20.5
w = 4.1
Write a proportion to find the width w.
Find the cross products.
Divide.The photo is 7.2 in. long and 4.1 in. wide.
Try This: Example 2
Course 2
5-7 Scale Drawings and Scale Models
Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is . Find the size of the dollhouse.
1.51
Think: dollhouseblueprint
= 1.51
l = 45 · 1.5
l = 67.5
Write a proportion to find the length l.
Find the cross products.
Multiply.
l 45
= 1.51
Try This 2 Continued
Course 2
5-7 Scale Drawings and Scale Models
w 24
= 1.51
w = 24 · 1.5
w = 36
Write a proportion to find the width w.
Find the cross products.
Multiply.The dollhouse is 67.5 inches long and 36 inches wide.
Think: dollhouseblueprint
= 1.51
Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is . Find the size of the dollhouse.
1.51
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?
Additional Example 3: Measurement Application
Course 2
5-7 Scale Drawings and Scale Models
Let d be the actual distance between the cities.1.560
= 7.5d
1.5 · d = 60 · 7.5
1.5d = 450
1.5d1.5
= 4501.5
d = 300The distance between the cities is 300 miles.
Write a proportion.
Find the cross products.
Multiply.
Divide.
Try This: Example 3
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Course 2
5-7 Scale Drawings and Scale Models
On a road map, the distance between Dallas and Houston is 7 inches. What is the actual distance between the cities if the map scale is 1 inch = 50 kilometers?
Let d be the actual distance between the cities.1
50= 7
d1 · d = 50 · 7
1d = 350
d = 350
The distance between the cities is 350 kilometers.
Write a proportion.
Find the cross products.
Multiply.
Lesson Quiz: Part 1
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Course 2
5-7 Scale Drawings and Scale Models
Identify the scale factor.
Statue of Liberty Model
Height (in.) 1,824 8
1.
2.
144 inches, or 12 feet
1228
On a scale drawing, a kitchen wall is 6 inches long.
The scale factor is . What is the length of the
actual wall?
124
Lesson Quiz: Part 2
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Course 2
5-7 Scale Drawings and Scale Models
3. On a road map, the distance from Green Bay toChicago is 11 cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km?
330 km