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4 January, 15:54

a rectangular field has a perimeter of 500m and an area of 14400m2. Find the lengths of the sides

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  1. 4 January, 17:53
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    Perimeter = 500 = 2x + 2y, where x and y are the length and width

    area = 14400 = xy

    x = 14400 / y

    substitute:

    500 = (2 * (14400/y)) + 2y

    [multiply by y]

    500y = 28800 + 2y^2

    2y^2 - 500y + 28800 = 0

    y^2 - 250y + 14400 = 0

    use the quadratic equation: y = (-b ± (b^2 - 4*a*c) ^1/2) / 2a

    the answers should be written in the form (y - answer one) (y - answer two)

    substitute these answers into x = 14400 / y to find x

    remember x and y can not be negative as they are lengths
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