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16 April, 07:43

The shorter leg of a right triangle is 8 centimeters less than the other leg. Find the length of the two legs if the hypotenuse is 40.

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  1. 16 April, 07:46
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    Long leg = x

    short leg = x - 8

    hypo = 40

    x^2 + (x-8) ^2 = 40^2

    x^2 + x^2 - 16x + 64 = 1600

    2x^2 - 16x - 1536 = 0

    2 (x^2 - 8x - 768) = 0

    (x - 32) (x + 24) = 0

    x - 32 = 0; x = 32

    x + 24 = 0; x = - 24

    so

    long leg = 32

    short leg = 32 - 8 = 24
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