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Calculating Actual Measurements from Scale Drawings in Blueprints

This lesson explores how to derive actual measurements from scale drawings using blueprints. For example, given a living room represented as 4 inches by 3 inches on a blueprint with a scale of 8 feet, students learn to calculate the actual dimensions of the room. By employing cross-multiplication and simplification, learners find the living room's actual length of 64 feet and width of 48 feet. Additionally, the lesson includes examples of map distances, enhancing understanding of using proportions in real-world applications.

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Calculating Actual Measurements from Scale Drawings in Blueprints

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  1. 1 2 Let = the actual length of the living room. 1 2 blueprint measure (in.) actual measure (ft) blueprint length (in.) actual length (ft) 4 = 8 COURSE 3 LESSON 5-7 Scale Models and Maps On a blueprint, the living room is 4 in. by 3 in. The scale is in. = 8 ft. What are the length and width of the actual living room? First, find the actual length of the living room. 5-7

  2. 1 2 • = 8 • 4 Write the cross products. 1 2 Simplify. = 32 1 2 32 Divide each side by . = 1 2 1 2 1 2 Simplify. = 64 COURSE 3 LESSON 5-7 Scale Models and Maps (continued) 5-7

  3. 1 2 blueprint measure (in.) actual measure (ft) blueprint length (in.) actual length (ft) 3 = 8 w COURSE 3 LESSON 5-7 Scale Models and Maps (continued) The length of the actual room is 64 ft. Next, find the actual width of the living room. Let w = the actual width of the living room. 5-7

  4. 1 2 • w = 8 • 3 Write the cross products. 1 2 Simplify. w = 24 1 2 w 24 Divide each side by . = 1 2 1 2 1 2 Simplify. w = 48 COURSE 3 LESSON 5-7 Scale Models and Maps (continued) The width of the actual room is 48 ft. 5-7

  5. map (cm) actual measure (km) 1 map (cm) actual (km) 7.5 = x 50 1 • x = 50 • 7.5 Write the cross products. x = 375 Simplify. COURSE 3 LESSON 5-7 Scale Models and Maps The map distance from El Paso, Texas, to Chihuahua, Mexico, measures about 7.5 cm. The scale is 1 cm = 50 km. Find the actual distance using a proportion. Let x = the actual distance. The distance from El Paso to Chihuahua is 375 km. 5-7

  6. COURSE 3 LESSON 5-7 Scale Models and Maps 1. A 6-ft man is designing a new chair that would make him feel like a 2.5-ft child. The seat of a normal chair is 1.5 ft high. How high should he make the seat in his new chair? 2. A map scale shows 4 cm to represent 6 km. Two intersections measure 1 cm apart on the map. What is the actual distance? 3.6 ft 1.5 km 5-7

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