Warm Up

Solve each proportion.x

7535

=1. 2.48

6x

=2.

x6

9 27

=3. 87

x3.5

=4.

x = 45 x = 20

x = 2 x = 4

Vocabulary

Scale

Scale drawing

Scale model

Scale factor

Indirect Measurement

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.

Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length?

Class Example

Write a proportion using the scale. Let x be the actual length of the amoeba.

1000 x = 1 8 The cross products are equal.

x = 0.008

The actual length of the amoeba is eight thousandths of a millimeter.

1000 1 = 8 mm

x mm

Solve the proportion.

Under a 10,000:1 microscope view, a fiber appears to have length of 1 mm. What is its actual length?

Partner Practice

Write a proportion using the scale. Let x be the actual length of the fiber.

10,000 x = 1 1 The cross products are equal.

x = 0.0001

The actual length of the fiber is 1 ten-thousandths of a millimeter.

10,000 1 = 1 mm

x mm

Solve the proportion.

Scale factor is the ratio of a length on a scale drawing or model to the corresponding length on the actual object.

The scale a:b is read “a to b.” For example, the scale 1 cm:4 m is read “one centimeter to four meters.”

Reading Math

When finding a scale factor, you must use the same measurement units. You can use a scale factor to find unknown dimensions.

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?

Class Practice

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

A model of a 27 ft tall house was made using a scale of 2 in.:3 ft. What is the height of the model?

Partner Practice

Find the scale factor.

The scale factor for the model is . Now set up a proportion.

118

2 in.3 ft

= 2 in.36 in.

= 1 in.18 in.

= 118

324 = 18h

Convert: 27 ft = 324 in.

Find the cross products.

18 = hThe height of the model is 18 in.

Divide both sides by 18.

118

= h in.324 in.

Convert to same measurements

What is “h”???Let h equal the height of the model.

A DNA model was built using the scale 5 cm: 0.0000001 mm. If the model of the DNA chain is 20 cm long, what is the length of the actual chain?

Individual Practice

The scale factor for the model is 500,000,000. This means the model is 500 million times larger than the actual chain.

5 cm 0.0000001 mm

50 mm 0.0000001 mm= = 500,000,000

Find the scale factor.

Individual Practice...continued

500,000,000 1

20 cm x cm= Set up a proportion.

500,000,000x = 1(20)

x = 0.00000004

The length of the DNA chain is 4 10-8 cm.

Find the cross products.

Divide both sides by 500,000,000.

How is scale different than rate?

Discuss with your partner

Write an answer (in words)

Sometimes, distances cannot be measured directly. One way to find such a distance is to use indirect measurement, a way of using similar figures and proportions to find a measure.

Class Practice

Triangles ABC and EFG are similar. Find the length of side EG.

B

A C

3 ft

4 ft

F

E G

9 ft

x

= Set up a proportion.

Substitute 3 for AB, 4 for AC, 9 for EF, and x for EG.

3x = 36 Find the cross products.

34 = 9

x

3x3

=36 3

Divide both sides by 3.

ABAC

EFEG

The length of side EG is 12 ft.

Divide both sides by 3. x = 12

Individual Practice

Triangles DEF and GHI are similar. Find the length of side HI.

2 in

E

D F

7 in

H

G I

8 in

x

DEEF = GH

HI Set up a proportion.

Substitute values for DE, EF, GH, and HI.2x = 56

The length of side HI is 28 in.

x = 28

27 = 8

x

2x2 = 56

2Find the cross products and solve for x.