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Math

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A Quadratic Word Problem

The length of a rectangular garden is 4 yards more than the width. The area of the garden is 60 square yards. Find the dimensions of the garden.

  • Math - ,

    W = Garden width

    H = Garden height

    A = Garden area


    L = W + 4

    A = L * W

    60 = ( W + 4 ) * W

    60 = W ^ 2 + 4 W Add 4 to both sides

    64 = W ^ 2 + 4 W + 4

    ________________________________________

    Remark :

    W ^ 2 + 4 W + 4 = ( W + 2 ) ^ 2

    ________________________________________


    64 = ( W + 2 ) ^ 2

    W + 2 = sqrt ( 64 )

    W + 2 = + OR - 8 Subtract 2 to both sides

    W + 2 - 2 = + OR - 8 - 2

    W = + OR - 8 - 2

    Solutions :

    W = 8 - 2 = 6

    and

    W - 8 - 2 = - 10

    Width can't be negative so :

    W = 6 in

    L = W + 4 = 6 + 4 = 10 in

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