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12 April, 11:30

A rectangular garden originally measured 5 feet by 10 feet as shown below. a path was created by increasing each side of the original rectangle by x-feet on both sides. if the area of the path that rings the garden is 54 square feet, find the value of x.

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  1. 12 April, 15:26
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    The area is given by

    A = (5 + 2x) * (10 + 2x) - 50

    Rewriting we have:

    A = 50 + 10x + 20x + 4x ^ 2 - 50

    Rewriting we have:

    A = 4x ^ 2 + 30x

    Substituting the value of the area we have:

    54 = 4x ^ 2 + 30x

    Rewriting:

    4x ^ 2 + 30x - 54 = 0

    We look for the roots:

    x1 = - 9

    x2 = 3/2

    We take the positive root:

    x2 = 3/2

    Answer:

    the value of x is:

    x = 3/2
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