1. Holt CA Course 1 5-8Scale Drawings and Scale Models NS1.3 Use proportions to solve problems (e.g., determine the value of N if T =, find the length of a side of a polygon similar to a known polygon). Use cross- multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. California Standards 4747 N 21

2. Holt CA Course 1 5-8Scale Drawings and Scale Models This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO gauge model train is. 1 87 This means that each dimension of the model is of the corresponding dimension of the actual train. 1 87

3. Holt CA Course 1 5-8Scale Drawings and Scale Models A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train. A scale drawing is a proportional two- dimensional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

4. Holt CA Course 1 5-8Scale Drawings and Scale Models Identify the scale factor. Teacher Example 1: Finding a Scale Factor RoomBlueprint Length (in.)14418 Width (in.)10813.5 blueprint length room length = 1818 1818 The scale factor is. Write a ratio. Then simplify. 18 144 = You can use the lengths or widths to find the scale factor. blueprint width room width = 1818 Write a ratio. Then simplify. 13.5 108 =

5. Holt CA Course 1 5-8Scale Drawings and Scale Models Student Practice 1: Identify the scale factor. Model AircraftBlueprint Length (in.)122 Wing span (in.)183 blueprint length aircraft length = 2 12 = 1616 Write a ratio. Then simplify. The scale factor is. 1616 blueprint wing span aircraft wing span = 3 18 = 1616 Write a ratio. Then simplify.

6. Holt CA Course 1 5-8Scale Drawings and Scale Models A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is. Find the size of the original photograph to the nearest tenth of an inch. Teacher Example 2: Using Scale Factors to Find Unknown Lengths 5151 Think: poster photo = 5151 36 l = 5151 5l = 36 l = 7.2 Write a proportion to find the length l. Find the cross products. Divide.

7. Holt CA Course 1 5-8Scale Drawings and Scale Models A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is. Find the size of the photograph. Teacher Example 2 Continued: 5151 Think: poster photo = 5151 20.5 w = 5151 5w = 20.5 w = 4.1 Write a proportion to find the width w. Find the cross products. Divide. The photo is 7.2 in. long and 4.1 in. wide.

8. Holt CA Course 1 5-8Scale Drawings and Scale Models Student Practice 2: Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is. Find the size of the dollhouse. 1.5 1 Think: dollhouse blueprint = 1.5 1 l = 45 · 1.5 l = 67.5 Write a proportion to find the length l. Find the cross products. Multiply. l 45 = 1.5 1

9. Holt CA Course 1 5-8Scale Drawings and Scale Models Student Practice 2: w 24 = 1.5 1 w = 24 · 1.5 w = 36 Write a proportion to find the width w. Find the cross products. Multiply. The dollhouse is 67.5 inches long and 36 inches wide. Think: dollhouse blueprint = 1.5 1 Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is. Find the size of the dollhouse. 1.5 1

10. Holt CA Course 1 5-8Scale Drawings and Scale Models On a road map with a scale of 1.5 inches = 60 miles, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities? Teacher Example 3: Measurement Application Let d be the actual distance between the cities. 1.5 60 = 7.5 d 1.5 · d = 60 · 7.5 1.5d = 450 1.5d 1.5 = 450 1.5 d = 300 The distance between the cities is 300 miles. Write a proportion. Find the cross product. Multiply. Divide both sides by 1.5.

11. Holt CA Course 1 5-8Scale Drawings and Scale Models Student Practice 3: On a road map with a scale of 1 inch = 50 kilometers, the distance between Dallas and Houston is 7 inches. What is the actual distance between the two cities? Let d be the actual distance between the cities. 1 50 = 7d7d 1 · d = 50 · 7 1d = 350 d = 350 The distance between the cities is 350 kilometers. Write a proportion. Find the cross products. Multiply.

12. Holt CA Course 1 5-8Scale Drawings and Scale Models Lesson Quiz Identify the scale factor. Statue of LibertyModel Height (in.) 1,8248 1. 2. 144 inches, or 12 feet 1 228 On a scale drawing, a kitchen wall is 6 inches long. The scale factor is. What is the length of the actual wall? 1 24 3. On a road map, the distance from Green Bay to Chicago is 11 cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km? 330 km