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20 April, 05:05

The length of a rectangle is 5 inches more then the width. the area of the rectangle is equal to 2 inches more than 4 times the perimeter. Find the length and width of the rectangle

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  1. 20 April, 05:07
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    P = 2 (L + W)

    L = W + 5

    A = 4P + 2

    P = 2 (W + 5 + W)

    P = 2 (2W + 5)

    P = 4W + 10

    A = 4P + 2

    A = 4 (4W + 10) + 2

    A = 16W + 42

    A = L * W

    A = W (W + 5)

    A = W^2 + 5W

    W^2 + 5W = 16W + 42

    W^2 + 5W - 16W - 42 = 0

    W^2 - 11W - 42 = 0

    (W + 3) (W - 14) = 0

    W - 14 = 0

    W = 14 <==

    L = W + 5

    L = 14 + 5

    L = 19 <==

    P = 2 (19 + 14)

    P = 2 (33)

    P = 66

    A = L * W

    A = 19 * 14

    A = 266

    answer : length = 19, width = 14 ... perimeter = 66 ... area = 266
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