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20 April, 03:43

Rachel has an 80:1 scale drawing of the floor plan of her house. On the floor plan, the dimensions of her rectangular living room are 1 7/8 by 2 1/2 inches. What is the area of her actual living room in square feet?

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  1. 20 April, 04:07
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    208⅓ ft²

    Step-by-step explanation:

    The dimensions of Rachel's living room are 80 times the measurements on the scale drawing.

    Calculate the width:

    w = 80 * 1⅞

    Convert the mixed number to an improper fraction = 80 * 15/8

    Cancel the 8s = 10 * 15

    = 150 in

    Convert inches to feet = 150/12

    Convert the improper fraction to a mixed number = (144 + 6) / 12

    = 12⁶/₁₂

    Reduce the fraction to lowest terms = 12½ ft

    Calculate the length

    l = 80 * 2½ = 80 * 5/2 = 40 * 5 = 200 in = 200/12 = (192 + 8) / 12

    l = 16⁸/₁₂ = 16⅔ ft

    Calculate the area

    A = lw

    A = 16⅔ * 12½

    Convert the mixed numbers to improper fractions

    A = 50/3 * 25/2

    Cancel the 2s

    = 25/3 * 25

    Multiply numerators and denominators

    = 625/3

    Convert the improper fraction to a mixed number

    = (624 + 1) / 3

    = 208⅓ ft²

    The area of Rachel's living room is 208⅓ ft².
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