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13 September, 15:56

A rectangular shaped garden has a perimeter of 66ft and area of 216ft. Find the dimensions

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  1. 13 September, 17:59
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    The perimeter is then

    2L + 2W = 66

    The area is

    L*W = 216

    Solve the first equation for L

    2L = 66 - 2W

    L = 66/2 - 2W/2 = 33 - W

    Put this into the second equation

    (33 - W) * W = 216

    33W - W^2 = 216

    rearranging

    W^2 - 33W + 216 = 0

    Using the quadratic formula

    [ - (-33) plus or minus sqrt ((-33) * (-33) - 4 * 1 * 216) ]/2

    [33 plus or minus sqrt (1089 - 864) ]/2

    [33 plus or minus sqrt (225) ]/2

    [33 plus or minus 15]/2

    (33 + 15) / 2 = 48/3 = 16 = W

    (33 - 15) / 2 = 18/2 = 9 = W

    Checking back into the original equations

    L = 24 W = 9
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