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16 November, 09:51

The hypotenuse of a right triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. Find the lengths of the legs of the triangle.

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  1. 16 November, 10:10
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    Let the shortest leg be x feet;

    The other leg will be (x + 14) feet.

    Using Pythagoras theorem;

    x^2 + (x+14) ^2 = 26^2

    x^2 + x^2 + 28x + 196 = 676

    2x^2 + 28x - 480 = 0

    x^2 + 14x - 240 = 0

    x^2 + 24x - 10x - 240 = 0

    x (x+24) - 10 (x+24) = 0

    (x+24) (x-10) = 0;

    x=10;

    x+14 = 24

    Hence, the length of the legs are 10 feet and 24 feet.
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