7-7 Scale Drawings Warm Up Problem of the Day Lesson Presentation Pre-Algebra

7-7 Scale Drawings Warm Up Evaluate the following for x = 16. Pre-Algebra 7-7 Scale Drawings Warm Up Evaluate the following for x = 16. 1. 3x 2. x Evaluate the following for x = . 3. 10x 4. x 3 4 48 12 2 5 1 4 1 10 4

Problem of the Day An isosceles triangle with a base length of 6 cm and side lengths of 5 cm is dilated by a scale factor of 3. What is the area of the image? 108 cm2

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

Vocabulary scale drawing scale reduction enlargement

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.

1 unit on the drawing is 20 units. 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 4 1 4 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

Additional Example 1A: Using Proportions to Find Unknown Scales or Lengths 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 cm x m 2 cm 8 m Set up proportion using scale length . actual length = 1  8 = x  2 Find the cross products. 8 = 2x 4 = x Solve the proportion. The scale is 1 cm:4 m.

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

Try This: Example 1A 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? 1 cm x m 4 cm 12 m Set up proportion using scale length . actual length = 1  12 = x  4 Find the cross products. 12 = 4x 3 = x Solve the proportion. The scale is 1 cm:3 m.

Try This: Example 1B 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? 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.

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.

Additional Example 2: Life Sciences Application Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length? 1000 1 = 8 mm x mm scale length actual length 1000  x = 1  8 Find the cross products. x = 0.008 Solve the proportion. The actual length of the amoeba is 0.008 mm.

Try This: Example 2 Under a 10,000:1 microscope view, a fiber appears to have length of 1mm. What is its actual length? 10,000 1 = 1 mm x mm scale length actual length 10,000  x = 1  1 Find the cross products. x = 0.0001 Solve the proportion. The actual length of the fiber is 0.0001 mm.

A drawing that uses the scale in. = 1 ft is said to be in in. scale 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 2

Additional Example 3A: Using Scales and Scale Drawings to Find Heights A. If a wall in a in. scale drawing is 4 in. tall, how tall is the actual wall? 1 4 0.25 in. 1 ft = 4 in. x ft. scale length actual length Length ratios are equal. Find the cross products. 0.25  x = 1  4 Solve the proportion. x = 16 The wall is 16 ft tall.

Additional Example 3B: Using Scales and Scale Drawings to Find Heights 1 2 B. How tall is the wall if a in. scale is used? 0.5 in. 1 ft = 4 in. x ft. scale length actual length Length ratios are equal. Find the cross products. 0.5  x = 1  4 Solve the proportion. x = 8 The wall is 8 ft tall.

Try This: Example 3A A. If a wall in a in. scale drawing is 0.5 in. thick, how thick is the actual wall? 1 4 0.25 in. 1 ft = 0.5 in. x ft. scale length actual length Length ratios are equal. Find the cross products. 0.25  x = 1  0.5 Solve the proportion. x = 2 The wall is 2 ft thick.

Try This: Example 3A Continued 1 2 B. How thick is the wall if a in. scale is used? 0.5 in. 1 ft = x ft. scale length actual length Length ratios are equal. Find the cross products. 0.5  x = 1  0.5 Solve the proportion. x = 1 The wall is 1 ft thick.

Lesson Quiz 1. What is the scale of a drawing in which a 9 ft wall is 6 cm long? 2. Using a in. = 1 ft scale, how long would a drawing of a 22 ft car be? 3. The height of a person on a scale drawing is 4.5 in. The scale is 1:16. What is the actual height of the person? The scale of a map is 1 in. = 21 mi. Find each length on the map. 4. 147 mi 5. 5.25 mi 1 cm = 1.5 ft 1 4 5.5 in. 72 in. 7 in. 0.25 in.