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  1. #1
    RSPRAGGS
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    Red face [SOLVED] help

    one leg of a right triangle is 7 feet shorter then then other leg. the hypotenuse is 2 feet longer then the longer leg. find the lengths of all three sides of the right triangle. this shorter then is throwing me for a loop. somebody help me .please
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  2. #2
    Site Founder MathMan's Avatar
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    I think this is it

    I think this is how you do it, somebody correct me if I'm wrong.

    one leg of a right triangle is 7 feet shorter then then other leg. => x-7
    the hypotenuse is 2 feet longer then the longer leg => x+2
    So the two sides are x, x-7, and the hypotenuse is x+2

    By Pathagores theorum we know that (a^2)+(b^2)=(c^2)

    So we have:
    (x^2)+(x-7)^2 = (x+2)^2

    we then get:
    x^2 + x^2 -14x +49 = x^2 +4x +4

    Simplifies to:
    x^2 -18x +45 = 0

    We factor to get:
    (x-3)(x-15) = 0

    So x can equal 3 or 15

    Since one side is 7 less than x and we cant have negative length 3 cannot be an answer. So one side is 15, the other is 8, and the hypotonus is 17.
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