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10 August, 21:37

A rectangular balcony has a perimeter of 24 feet and an area of 27 square feet. what are the dimensions of the balcony?

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  1. 10 August, 21:43
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    Let x and y be the dimensions of the rectangular balcony.

    The perimeter is 24 ft, therefore

    2 (x + y) = 24

    or

    x + y = 12 (1)

    The area is 27 ft², therefore

    xy = 27

    or

    y = 27/x (2)

    Substitute (2) into (1).

    x + 27/x = 12

    Multiply through by x.

    x² + 27 = 12x

    x² - 12x + 27 = 0

    (x - 3) (x - 9) = 0

    x = 3 or x = 9

    When x = 3, y = 27/3 = 9

    When x = 9, y = 27/9 = 3

    Answer:

    The dimensions are 3ft by 9 ft.
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