Pre-Algebra

7-7 Scale Drawings

Learn to make comparisons between and find dimensions of scale drawings and actual objects.

Pre-Algebra

7-7 Scale Drawings

A scale drawing is a two-dimensional drawing that accurately represents an object. The scale drawing is mathematically similar 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.

Pre-Algebra

7-7 Scale Drawings

Pre-Algebra

7-7 Scale Drawings

Pre-Algebra

7-7 Scale Drawings

Pre-Algebra

7-7 Scale Drawings

A scale drawing is a two-dimensional drawing that accurately represents an object. The scale drawing is mathematically similar 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.

Pre-Algebra

7-7 Scale Drawings

The scale a:b is read “a to b.” For example, the scale 1 cm:3 ft is read “one centimeter to three feet.”

Reading Math

Scale Interpretation

1:20 1 unit on the drawing is 20 units.

1 cm: 1 m 1 cm on the drawing is 1 m.

in. = 1 ft in. on the drawing is 1 ft.1 41 4

Pre-Algebra

7-7 Scale Drawings

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?

Example 1A: Using Proportions to Find Unknown Scales or Lengths

1 cmx m = 2 cm

8 m Set up proportion using scale length .actual length

1 8 = x 2 Find the cross products.

8 = 2x

Solve the proportion.

The scale is 1 cm:4 m.

4 = x

Pre-Algebra

7-7 Scale Drawings

B. The length of an object on a scale drawing is 1.5 inches. The scale is 1 in:6 ft. What is the actual length of the object?

Example 1B: Using Proportions to Find Unknown Scales or Lengths

1 in.6 ft = 1.5 in.

x ft Set up proportion using scale length .actual length

1 x = 6 1.5 Find the cross products.

x = 9 Solve the proportion.

The actual length is 9 ft.

Pre-Algebra

7-7 Scale Drawings

A scale drawing that is smaller than the actual object is called a reduction. A scale drawing can also be larger than the object. In this case, the drawing is referred to as an enlargement.

Pre-Algebra

7-7 Scale Drawings

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

Example 2: Life Sciences Application

scale length actual length

1000 x = 1 8 Find the cross products.

x = 0.008

The actual length of the amoeba is 0.008 mm.

1000 1 = 8 mm

x mm

Solve the proportion.

Pre-Algebra

7-7 Scale Drawings

A scale drawing is a two-dimensional drawing that accurately represents an object. The scale drawing is mathematically similar 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.

Pre-Algebra

7-7 Scale Drawings

Pre-Algebra

7-7 Scale Drawings

A. 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?

Try This: Example 1A

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

Solve the proportion.

The scale is 1 cm:3 m.

3 = x

Pre-Algebra

7-7 Scale Drawings

B. The length of an object on a scale drawing is 2 inches. The scale is 1 in:4 ft. What is the actual length of the object?

Try This: Example 1B

1 in.4 ft = 2 in.

x ft Set up proportion using scale length .actual length

1 x = 4 2 Find the cross products.

x = 8 Solve the proportion.

The actual length is 8 ft.

Pre-Algebra

7-7 Scale Drawings

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

Try This: Example 2

scale length actual length

10,000 x = 1 1 Find the cross products.

x = 0.0001

The actual length of the fiber is 0.0001 mm.

10,000 1 = 1 mm

x mm

Solve the proportion.

Pre-Algebra

7-7 Scale Drawings

A drawing that uses the scale in. = 1 ft is

said to be in in. scale. Similarly, a

drawing that uses the scale in. = 1 ft is in

in. scale.

1 4

1 4

1 2

1 2

Pre-Algebra

7-7 Scale Drawings

Example 3A: Using Scales and Scale Drawings to Find Heights

scale length actual length

0.25 x = 1 4 Find the cross products.

x = 16

The wall is 16 ft tall.

0.25 in. 1 ft = 4 in.

x ft.

A. If a wall in a in. scale drawing is 4 in. tall, how tall is the actual wall?

14

Length ratios are equal.

Solve the proportion.

Pre-Algebra

7-7 Scale Drawings

B. How tall is the wall if a in. scale is used?

Example 3B: Using Scales and Scale Drawings to Find Heights

12

scale length actual length

0.5 x = 1 4 Find the cross products.

x = 8

The wall is 8 ft tall.

0.5 in. 1 ft = 4 in.

x ft.Length ratios are equal.

Solve the proportion.

Pre-Algebra

7-7 Scale Drawings

A scale drawing is a two-dimensional drawing that accurately represents an object. The scale drawing is mathematically similar 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.

Pre-Algebra

7-7 Scale Drawings

Try This: Example 3A

scale length actual length

0.25 x = 1 0.5 Find the cross products.

x = 2

The wall is 2 ft thick.

0.25 in. 1 ft = 0.5 in.

x ft.Length ratios are equal.

Solve the proportion.

A. If a wall in a in. scale drawing is 0.5 in. thick, how thick is the actual wall?

14

Pre-Algebra

7-7 Scale Drawings

B. How thick is the wall if a in. scale is used?

Try This: Example 3A Continued

12

scale length actual length

0.5 x = 1 0.5 Find the cross products.

x = 1

The wall is 1 ft thick.

0.5 in. 1 ft = 0.5 in.

x ft.Length ratios are equal.

Solve the proportion.