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5-7 Scale Drawings and Scale Models Course 2 5-7 Scale Drawings and Scale Models Warm Up Write each fraction in the simplest form. 4 1 2. 9 1 1. 15 48 12 135 Convert the following measurements. 3. 192 inches = feet 16 4. 18.5 feet = inches 222 5. 324 inches = feet 27 Course 2 5-7 Scale Models and Scale Drawings 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 1 gauge model train is 87 . 1 This means that each dimension of the model is 87 of the corresponding dimension of the actual train. Course 2 5-7 Scale Models and Scale Drawings 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 drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent. Course 2 5-7 Scale Drawings and Scale Models Example 1: Finding a Scale Factor Identify the scale factor. Room Blueprint Length (in.) 144 18 Width (in.) 108 13.5 blueprint length = 18 Write a ratio using one of the room length 144 dimensions. = 1 Simplify. 8 The scale factor is 1 . 8 Course 2 5-7 Insert Drawings and Scale Models Scale Lesson Title Here Try This: Example 1 Identify the scale factor. Model Aircraft Blueprint Length (in.) 12 2 Wing span (in.) 18 3 blueprint length = 2 Write a ratio using one of aircraft length 12 the dimensions. = 1 Simplify. 6 The scale factor is 1 . 6 Course 2 5-7 Scale Drawings and Scale Models Example 2: Using Scale Factors to Find Unknown Lengths A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale 5 factor is 1 . Find the size of the photograph. poster = 5 Think: photo 1 36 = 5 Write a proportion to find the l 1 length l. 5l = 36 Find the cross products. l = 7.2 Divide. Course 2 5-7 Scale Drawings and Scale Models Example 2 Continued A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale 5 factor is 1 . Find the size of the photograph. poster = 5 Think: photo 1 20.5 = 5 Write a proportion to find the w 1 width w. 5w = 20.5 Find the cross products. w = 4.1 Divide. The photo is 7.2 in. long and 4.1 in. wide. Course 2 5-7 Scale Drawings and Scale Models Try This: Example 2 Katie’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 1.5. Find the size of the dollhouse. 1 dollhouse = 1.5 Think: blueprint 1 l = 1.5 Write a proportion to 45 1 find the length l. Find the cross l = 45 · 1.5 products. l = 67.5 Multiply. Course 2 5-7 Scale Drawings and Scale Models Try This: 2 Continued Ariel’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 1.5. Find the size of the dollhouse. 1 dollhouse = 1.5 Think: blueprint 1 w = 1.5 Write a proportion 24 1 to find the width w. w = 24 · 1.5 Find the cross products. w = 36 Multiply. The dollhouse is 67.5 inches long and 36 inches wide. Course 2 5-7 Scale Drawings and Scale Models Example 3: Measurement Application On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles? Let d be the actual distance between the cities. 1.5 = 7.5 Write a proportion. 60 d 1.5 · d = 60 · 7.5 Find the cross products. 1.5d = 450 Multiply. 1.5d = 450 Divide. 1.5 1.5 d = 300 The distance between the cities is 300 miles. Course 2 5-7 Insert Drawings and Scale Models Scale Lesson Title Here Try This: Example 3 On a road map, the distance between Dallas and Houston is 7 inches. What is the actual distance between the cities if the map scale is 1 inch = 50 kilometers? Let d be the actual distance between the cities. 1= 7 50 d Write a proportion. 1 · d = 50 · 7 Find the cross products. 1d = 350 Multiply. d = 350 The distance between the cities is 350 kilometers. Course 2 5-7 Scale Drawings andHere Models Insert Lesson Title Scale Assignment: pg. 290-291 1-13 All Course 2

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posted: | 8/18/2012 |

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