Scale Drawings & Proportions

A scale drawing is a two-dimensional drawing of an object that is proportional to the object.

A scale gives the ratio of the dimensions in the drawing to the dimensions of the object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units.

A scale model is a three-dimensional model that is proportional to the object.

SCALE DRAWINGS

•A scale drawing is a drawing of an object with dimensions proportional to those of the actual object. To find lengths from scale drawings, set up and solve proportions.

There are many uses of ratios and proportions. We use them in map reading, making scale drawings and models, solving problems.

The most recognizable use of ratios and proportions is drawing models and plans for construction. Scales must be used to approximate what the actual object

will be like.

Example 1: Find Actual Measurements

A set of landscape plans shows a flower bed that is 6.5 inches wide. The scale on the plans is 1 inch = 4 feet.

What is the width of the actual flower bed?Let x represent the actual width of the flower bed. Write and

solve a proportion. Plan width----> 1 inch = 6.5 inches<---plan widthActual width--> 4 feet x feet <-----actual width 1x = 46.5 cross products

x= 26 The actual flower bed width is 26 feet.

SCALE DRAWINGS USING PROPORTIONS

¼ in = 5 ft is a scale for a rock band’s concert stage.

The scale length of the drum stand is 1 inch.

What is the actual length of the drum stand?

)(

)(

)(

)(

actualobject

drawingobject

ftactual

indrawing

x

1

5

25.

Cross multiply. 1525. x525. x

.25 .25

20x

Divide by .25

SCALE DRAWINGS USING PROPORTIONS

¼ in = 5 ft is a scale for a rock band’s concert stage.

The actual length of the microphone stand is 4.5 feet. What is the length mic stand in the drawing?

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)(

)(

)(

actualobject

drawingobject

ftactual

indrawing

5.45

25. x

Cross multiply. x 55.425.x5125.1

5 5

inchesx 225.0

Divide by 5.

SCALE DRAWINGS USING PROPORTIONS

Given a scale of 0.5 in = 4 ft, find the actual length for A and find the drawing length for B.

x

75.2

4

5.

75.245. x115. x

.5 .5

ftx 22

inA4

32) ftB 5)

54

5. x

x 455.

x45.2 4 4

ftx 625.0

A. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale?

1 cmx m = 2 cm

8 m1 8 = x 2 Find the cross products.

8 = 2x

Divide both sides by 2.

The scale is 1 cm:4 m.

4 = x

Set up proportion using scale length .actual length

The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale?

1 cmx m = 4 cm

12 m Set up proportion using scale length .actual length

1 12 = x 4 Find the cross products.12 = 4x

Divide both sides by 4.

The scale is 1 cm:3 m.

3 = x