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12 April, 19:18

On a set of blueprints for a new home, the contractor has established a scale of 0.5in : 10 ft. What are the dimensions on the blueprints of a bedroom that will be 18 feet by 16 feet.

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  1. 12 April, 19:23
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    The dimensions on the blueprints are 0.9 inches and 0.8 inches

    Step-by-step explanation:

    * Lets explain the relation between the drawing dimensions and

    the real dimensions

    - A scale drawing make a real object with accurate sizes reduced

    or enlarged by a certain amount called the scale

    - Ex: If the scale drawing is 1 : 10, so anything drawn with the size of

    1 have a size of 10 in the real so a measurement of 15 cm on the

    drawing will be 150 cm on the real

    - In a scale drawing, all dimensions have been reduced by the same

    proportion

    * Lets solve the problem

    - On a set of blueprints for a new home, the contractor has

    established a scale of 0.5 in : 10 ft

    ∵ The drawing scale ratio must be in same unit

    ∴ Change the feet to inch

    ∵ 1 foot = 12 inches

    ∴ 10 feet = 10 * 12 = 120 inches

    ∴ The scale is 0.5 inches : 120 inches

    - Simplify the scale by multiply it by 2

    ∴ The scale is 1 in : 240 in

    - Lets find the dimensions on the blueprints

    ∵ The real dimensions are 18 feet and 16 feet

    - Change the feet to inches

    ∴ 18 feet = 18 * 12 = 216 inches

    ∵ 16 feet = 16 * 12 = 192 inches

    ∵ The scale is 1 : 240

    ∴ 1/240 = x/216 ⇒ use cross multiplication

    ∴ 240 x = 216 divide both sides by 240

    ∴ x = 0.9 inch

    ∵ The scale is 1 : 240

    ∴ 1/240 = y/192 ⇒ use cross multiplication

    ∴ 240 y = 192 divide both sides by 240

    ∴ y = 0.8 inch

    * The dimensions on the blueprints are 0.9 inches and 0.8 inches
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