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31 December, 03:56

The shorter leg of a right triangle is 8 less than the hypotenuse. The longer leg is 1 less than the hypotenuse. Find the perimeter of the triangle.

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  1. 31 December, 07:20
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    Perimeter is 30

    Explanation:

    short leg = h - 8

    longer leg = h - 1

    (h-8) ^2 + (h - 1) ^2 = h^2

    h^2 - 16h + 64 + h^2 - 2h + 1 = h^2

    h^2 - 16h + 64 + h^2 - 2h + 1 - h^2 = 0

    h^2 - 18h + 65 = 0

    (h - 13) (h - 5) = 0

    h-13 = 0 - --> h = 13 - --> short leg is 5 and long leg is 12 - --> perimeter is 30

    h-5 = 0 - --> h = 5 - -> short leg is - 3 and long leg is 4 <-- - disqualified because leg measure cannot be negative

    short leg is 5, long leg is 12, hypotneuse is 13

    5^2 + 12^2 = 25 + 144 = 169 = 13^2 <-- - pythagorean check

    perimeter is 5 + 12 + 13 = 30
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