Geometry

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The area of a rectangle is 72 square inches and the perimeter is 44 inches. Find its dimensions.

  • Geometry -

    One way to solve this is to find the factors of 72. Then see which of these will fit for the perimeter.

  • Geometry -

    let the length and width be x and y respectively
    then
    2x + 2y = 44
    x + y = 22
    y = 22-x

    area = xy = 72
    x(22-x) = 72
    22x - x^2 - 72 = 0
    x^2 - 22x + 72 = 0
    (x-4)(x-18) = 0
    x = 4 or x = 18

    if x = 4, then y = 22-4 = 18
    if x = 18, then y = 22-18 = 4

    the dimensions are 4 by 18 inches

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