SOLUTION: The hypotenuse of a right triangle is 25 km long the length of one leg is 17 km less than the other find the length of the legs

Question 860783: The hypotenuse of a right triangle is 25 km long the length of one leg is 17 km less than the other find the length of the legs
Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
x^2 + (x + 17)^2 = 25^2
x^2 + x^2 + 34x + 289 = 625
2x^2 + 34x - 336 = 0
x^2 + 17x - 168 = 0
(x + 24)(x - 7) = 0
x = -24, x = 7

x has to be positive, so the shorter leg is 7 km and the longer leg is 24 km.

Alternatively, remember that 7, 24, and 25 make up a Pythagorean triple.
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