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Proportionality

Lesson 11. Proportionality. Scale Drawings. Warm-Up. Use the similar parallelograms below. Find their scale factor. Find the ratio of their perimeters. Find the ratio of their areas. Two similar figures have a perimeter of 4 m and 28 m . Find their scale factor.

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Proportionality

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  1. Lesson 11 Proportionality Scale Drawings

  2. Warm-Up • Use the similar parallelograms below. • Find their scale factor. • Find the ratio of their perimeters. • Find the ratio of their areas. • Two similar figures have a perimeter of 4 m and 28 m. • Find their scale factor. • Find the ratio of their areas. • Two similar figures have a scale factor of 2 : 5. If the larger figure has a perimeter of 40 ft, what is the area of the smaller figure? 15 yd 24 yd

  3. Scale Drawings Target: Use scales for maps, blueprints and models to find missing measurements.

  4. Example 1a Alan’s map has a scale of 2 inches : 5 miles. The distance on the map from Mt. Hood Meadows to Alan’s home is 16 inches. What is the actual distance? • Write a proportion. • Use cross products to solve. 2x = 80 x = 40 • The actual distance is 40 miles.

  5. Example 1b Alan’s map has a scale of 2 inches : 5 miles. The actual distance from Alan’s home to Portland is 25 miles. Find the distance on the map. • Write a proportion. • Use cross products to solve. 5x = 50 x = 10 • The distance to Portland on the map is 10 inches.

  6. Example 2 A model car is made with a scale factor of 1 inch: 11 inches or 1 : 11. The actual car is 7 feet 4 inches long. How long is the model car? • Convert 7 feet 4 inches to inches to 7 ft 4 in = 7·12 + 4 match the scale factor: = 84 + 4 = 88 in • Write a proportion using the scale factor 1 : 11. • Use cross products to solve. 11x = 88 x = 8 • The model car is 8 inches long.

  7. Exit Problems A map has a scale of 2 inches : 5 miles. Use the given distance on a map to find the actual distance. • 8 in • 1 ft 2 in A model car has a scale of 1 : 24. • The model car is 4 inches long. How long is the actual car in inches? • How long is the actual car in feet?

  8. Communication Prompt When have you or a member of your family used a scale drawing? What information did it help you figure out?

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