7th Grade Math

286 Proportions and Similarity

Find a Scale Factor

SAILBOATS Find the scale factor of a model sailboat if the scale is

1 inch = 6 feet.

_1 inch

6 feet

= _1 inch

72 inches

Convert 6 feet to inches.

= _^1

72

Divide out the common units.

The scale factor is _^1

72

.

c. CARS What is the scale factor of a model car if the scale is

1 inch = 2 feet?

Construct a Scale Model

FERRIS WHEELS Penny is making a

15 in.

model of a Ferris wheel that is 60 feet

tall. The model is 15 inches tall. Penny

also is making a model of the sky

needle ride that is 100 feet tall using

the same scale. How tall is the model?

model

actual

_15 in.

60 ft

= _1 in.

4 ft

Divide the numerator and denominator by 15 so the

numerator equals 1.

The scale is 1 inch = 4 feet. Using this scale, find the height of the

sky needle ride.

model

actual

_1 in.

4 ft

= _x in.

100 ft

1 · 100 = 4 · x Find the cross products.

100 = 4 x Multiply.

25 = x Divide by 4.

The height of the sky needle model is 25 inches.

d. SOLAR SYSTEM Leah is constructing a scale model of the solar

system for science class. She knows the diameter of the Sun is

1,391,900 kilometers, but would like to make it 10 inches. If

Mercury’s orbit radius is 57,950,000 kilometers, how many feet

away from the Sun will Mercury be in the model?

Equivalent Scales Equivalent Scales

The scales below are

equivalent because their

scale factors are equal, _ 721.

• 1 inch = 6 feet


• 2 _^1 inch = 3 feet

284_291_C05_L2_895130.indd 286 12/29/09 1:01 PM