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20 July, 23:59

The area of the of a rectangle is 336 square inches. If the perimeter is 76. What is the shorter sides length?

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  1. 21 July, 01:26
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    hello:

    the perimeter is : p = 2 (w + l)

    The area is : A = w * l w : width l : length w?

    2 (w + l) = 76

    w * l = 336

    you have the system:

    w + l = 38 ... (1)

    w * l = 336 ... (2)

    by (1) : l = 38 - w

    subst in (2) : w (38 - w) = 336

    38w - w² = 336

    w² - 38w + 336 = 0

    delta = b² - 4ac when : a = 1 and b = - 38 c = 336

    delta = (-38) ² - 4 (1) (336) = 1444 - 1344 = 100 = 10²

    w1 = (38-10) / 2 = 14 (the shorter sides length)

    w2 = (38+10) / 2 = 24 (refused)
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