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18 December, 10:35

A sign in the shape of a right triangle has one leg that is 7 in longer than the other leg what is the length of the shorter leg if the perimeter is 30 in.

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  1. 18 December, 12:51
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    Let the shorter leg be x.

    Let the hypotenuse be y.

    The the longer leg is x + 7.

    The perimeter is 30.

    x + x + 7 + y = 30

    y = 30 - 2x - 7

    y = - 2x + 23

    The hypotenuse is - 2x + 23.

    Now we use the Pythagorean theorem.

    a^2 + b^2 = c^2

    x^2 + (x + 7) ^2 = (-2x + 23) ^2

    x^2 + x^2 + 14x + 49 = 4x^2 - 92x + 529

    2x^2 - 106x + 480 = 0

    x^2 - 53x + 240 = 0

    (x - 5) (x - 48) = 0

    x = 5 or x = 48

    Since 48 is greater than the perimeter, we discard that solution.

    x is the shorter leg.

    The shorter leg measures 5 units.
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