Holt CA Course 1

5-8 Scale Drawings and Scale Models

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California StandardsCalifornia Standards

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Holt CA Course 1

5-8 Scale Drawings and Scale Models

5. 324 inches = feet

Warm UpWrite each fraction in simplest form.

1. 4

482. 9

135

Convert the following measurements.

3. 192 inches = feet

4. 18.5 feet = inches

16

222

27

112

115

Holt CA Course 1

5-8 Scale Drawings and Scale Models

NS1.3 - Use proportions to solve NS1.3 - Use proportions to solve problems (e.g., determine the value of problems (e.g., determine the value of NN if = , find the length of a side if = , find the length of a side of a polygon similar to a known of a polygon similar to a known polygon). Use cross-multiplication as a polygon). Use cross-multiplication as a method for solving such problems,method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.

California Standards

4 4 77

NN 2121

Holt CA Course 1

5-8 Scale Drawings and Scale Models

Objective:Objective: You will learn how You will learn how to understand ratios and to understand ratios and proportions in scale drawings proportions in scale drawings and use ratios and proportions and use ratios and proportions with scale.with scale.

Holt CA Course 1

5-8 Scale Drawings and Scale Models

Vocabulary

scale modelscale factorscalescale drawing

Holt CA Course 1

5-8 Scale Drawings and Scale Models

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 . 187

This means that each dimension of the model is of the corresponding dimension of the actual train.

187

Holt CA Course 1

5-8 Scale Drawings and Scale Models

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.

A scale drawing is a proportional two-dimensional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

Holt CA Course 1

5-8 Scale Drawings and Scale Models

Identify the scale factor.

Example 1: Finding a Scale Factor

Room Blueprint

Length (in.) 144 18

Width (in.) 108 13.5

blueprint lengthroom length

= 18

1 8

The scale factor is .

Write a Write a ratio. Then ratio. Then simplify.simplify.

18144

=

You can use the lengths or widths to find the scale factor.

blueprint widthroom width

= 18

Write a ratio. Write a ratio. Then Then simplify.simplify.

13.5108

=

Holt CA Course 1

5-8 Scale Drawings and Scale ModelsCheck It Out! Example 2

Identify the scale factor.

Model Aircraft Blueprint

Length (in.) 12 2

Wing span (in.) 18 3

blueprint length aircraft length

= 212

= 16

Write a ratio. Write a ratio. Then Then simplify.simplify.

The scale factor is . 16

blueprint wing span aircraft wing span

= 318

= 16

Write a Write a ratio. Then ratio. Then simplify.simplify.

Holt CA Course 1

5-8 Scale Drawings and Scale Models

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 original photograph to the nearest tenth of an inch.

Example 3: Using Scale Factors to Find Unknown Lengths

15

Think: photo poster

= 15

l 36

= 15

5l = 36

l = 7.2

Write a Write a proportion to find proportion to find

the length the length ll..Find the Find the cross cross products.products.

Divide.Divide.

Holt CA Course 1

5-8 Scale Drawings and Scale Models

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.

Example 3 Continued

15

Think: photo poster

= 15

w 20.5

= 15

5w = 20.5

w = 4.1

Write a proportion Write a proportion to find the width to find the width w.w.

Find the Find the cross cross products.products.

Divide.Divide.

The photo is 7.2 in. long and 4.1 in. wide.

Holt CA Course 1

5-8 Scale Drawings and Scale ModelsCheck It Out! Example 4

24w

= 1 1.5

24 · 1.5 = w

36 = w

Write a proportion Write a proportion to find the width to find the width w.w.

Find the Find the cross cross products.products.

Multiply.Multiply.

The dollhouse is 67.5 inches long and 36 inches wide.

Think: blueprintdollhouse

= 1 1.5

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 1.5

Holt CA Course 1

5-8 Scale Drawings and Scale ModelsCheck It Out! Example 4 Continued

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 1.5

Think: blueprintdollhouse

= 1 1.5

45 · 1.5 = l67.5 = l

Write a proportion Write a proportion to find the length to find the length

ll..Find the cross Find the cross products.products.

Multiply.Multiply.

45

l = 1

1.5

Holt CA Course 1

5-8 Scale Drawings and Scale Models

On a road map with a scale of 1.5 inches = 60 miles, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities?

Example 5: Measurement Application

Holt CA Course 1

5-8 Scale Drawings and Scale Models

On a road map with a scale of 1.5 inches = 60 miles, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities?

Example 5: Measurement Application

Let d be the actual distance between the cities.

1.560

= 7.5d

1.5 · d = 60 · 7.5

1.5d = 4501.5d1.5

= 4501.5

d = 300The distance between the cities is 300 miles.

Write a Write a proportion.proportion.

Find the cross Find the cross product.product.

Multiply.Multiply.

Divide both Divide both sides by 1.5sides by 1.5

Holt CA Course 1

5-8 Scale Drawings and Scale ModelsCheck It Out! Example 6

On a road map with a scale of 1 inch = 50 kilometers, the distance between Dallas and Houston is 7 inches. What is the actual distance between the two cities?

Let d be the actual distance between the cities. 1 50

= 7d

1 · d = 50 · 7

1d = 350

d = 350

The distance between the cities is 350 kilometers.

Write a proportion.Write a proportion.

Find the cross products.Find the cross products.

Multiply.Multiply.

Holt CA Course 1

5-8 Scale Drawings and Scale Models

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Holt CA Course 1

5-8 Scale Drawings and Scale ModelsLesson Quiz

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

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