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13 January, 06:46

A college parking lot is 140 ft long and 90 ft wide. The college wants to increase the area of the lot by 29% by adding strips of equal width to one end and one side. (So, the new shape will be a larger rectangle.) Find the width of one such strip. Round your answer to the nearest integer.

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  1. 13 January, 09:42
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    The initial dimenssions of the park lot are:

    length: 140 ft

    width: 90 ft

    initial area: 140 * 90 = 12,600 ft^2

    Area increased 29% = 12,600 * 1.29 = 16,254 ft^2

    width of the strips: x

    New length: 140 + x

    New width: 90 + x

    New area: (140+x) (90+x) = 16,254

    Solution of the equation:

    12600 + 230x + x^2 = 16254

    => x^2 + 230x - 3654 = 0

    Use the quadratic formula.

    x = {-230 + / - √[ 230^2 - 4*1 * (-3654) ]} / 2 =

    x = 14.92

    The other solution is negative so it is discarded.

    Answer: 15 ft
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