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Lesson 6.5 Scale Drawings Students will be able to understand ratios and proportions in scale drawings.

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Warm Up Write each fraction in the simplest form Convert the following measurements: inches = ________ feet feet = ________ inches inches = ________ feet

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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 This means that each dimension of the model is of the corresponding dimension of the actual train. (1 inch on the model is 87 inches on the actual train.) 1 87

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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.

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Identify the scale factor. RoomBlueprint Length12 ft.18 in. Width9 ft.13.5 in. Blueprint Length Room Length = 18 in. 12 ft. Simplify. (Scale factor ratios must be written as a single unit rate) = The scale factor is: 1818 Remember from lesson 6.1 when common units (in.) are used the ratio will NOT have units! Units are like quantities (length to length). They must be converted to common units! Which unit will you convert? FEET to INCHES 12 ft x _____in. ft in. Now replace 12ft with 144 in. 18 in. 144 in. =

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Identify Scale Factor: Your Turn! RoomBlueprint Length8 ft.1 in. Width18 ft.2.25 in. Blueprint width Room width Blueprint length Room length Room width Blueprint width 2.25 in. 18 ft. Units are like quantities (length to length). They must be converted to common units! Which unit will you convert? FEET to INCHES 18 ft. x _________in. ft = 216 in in. 216 in. Simplify. (Scale factor ratios must be written as a single unit rate) 2.25 = 1 96 The scale factor is: 1 96

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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? Measurement Application Write a proportion Pittsburgh to Philadelphia (map) Pittsburgh to Philadelphia (actual) Scale (map) Scale (actual) Substitute Values 7.5 in. X miles 1.5 in. 60 miles Cross Products 7.5 x 60 = 1.5x 450 = 1.5x Divide Both sides by The distance between the cities is 300 miles.

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1 in. = 2 ft. Use the scale on the drawing to find the scale factor and the perimeter of the tree house. The scale is: 1 in. 2ft. 2 ft. x 12 in. 1 1 ft. = 24 in = 1 24 In. In. Scale factor = 1 24 Write a proportion to find the perimeter of the actual object. Perimeter of Drawing Perimeter of Actual object = 1in scale 2ft scale Substitute. 11 in. x ft. = 1 in. 2 ft. Use cross products. 11 x 2 = 1x 22 = x The actual perimeter of the tree house is 22 ft. Convert to same units for scale factor.

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Homework Time: Page 287 problems 1-16 all

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