Scale Drawings and Scale Models 4 6 Vocabulary

* Scale Drawings and Scale Models 4 -6

Vocabulary Scale drawing- a proportional two-dimensional drawing of an object. Scale factor- ratio that describes the relationship between the dimensions of the actual object and the scale drawing or model. Scale model- a proportional three- dimensional model of an object. Scale- the ratio between two sets of measurements.

Additional Example 1: Finding a Scale Factor Identify the scale factor. Length (in. ) Width (in. ) blueprint length = 18 144 room length = 1 8 The scale factor is 1. 8 Room 144 108 Blueprint 18 13. 5 Write a ratio using one of the dimensions. Simplify. Caution! A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions.

Check It Out: Example 1 Identify the scale factor. Model Aircraft Length (in. ) 12 Wing span (in. ) 18 Blueprint 2 3

Additional 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. 5 The scale factor is. Find the size of the 1 photograph. poster = 5 Think: photo 1 36 = 5 l 1 5 l = 36 l = 7. 2 Write a proportion to find the length l. Find the cross products. Divide.

Additional Example 2 Continued A photograph was enlarged and made into a poster. The poster is 20. 5 inches by 36 inches. The scale factor is 5. Find the size of the 1 photograph. Think: poster = 5 photo 1 20. 5 = 5 w 1 5 w = 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.

Check It Out: Example 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 1. 5 factor is 1. Find the size of the dollhouse.

Additional 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. 5 d = 450 Multiply. 1. 5 d = 450 Divide both sides by 1. 5 d = 300 The distance between the cities is 300 miles.

Check It Out: 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?