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3 June, 04:55

A rectangular yard has area 96 square feet. If the width of the yard is 4 ft less than length, what is the perimeter, in feet, of the yard?

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  1. 3 June, 06:21
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    Area of the rectangular yard = 96 square feet

    Let us assume the length of the yard = x feet

    Width of the yard = x - 4 feet

    Then

    Area of the yard = length * width

    96 = x (x - 4)

    96 = x^2 - 4x

    x^2 - 4x - 96 = 0

    x^2 - 12x + 8x - 96 = 0

    x (x - 12) + 8 (x - 12) = 0

    (x - 12) (x + 8) = 0

    As the value of length cannot be negative so

    x - 12 = 0

    x = 12

    So

    Length of the yard = 12 feet

    Width of the yard = x - 4 feet

    = 12 - 4 feet

    = 8 feet

    Then

    Perimeter of the yard = 2 (length + width)

    = 2 (12 + 8)

    = 2 * 20 feet

    = 40 feet.

    So the perimeter of the yard is 40 feet.
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