SOLUTION: I know the answer to this already but I don't know the proper way to solve for it so that is what i'm looking for here. The hypotenuse of a right triangle is 25m and the differe

Question 612610: I know the answer to this already but I don't know the proper way to solve for it so that is what i'm looking for here.
The hypotenuse of a right triangle is 25m and the difference between the lengths of the two legs are 17m what are the lengths of the two sides.

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The hypotenuse of a right triangle is 25m and the difference between the lengths of the two legs are 17m what are the lengths of the two sides.
.
Let x = length of one leg
then
x+17 = length of second leg
.
applying Pythagorean theorem
x^2 + (x+17)^2 = 25^2
x^2 + (x+17)(x+17) = 25^2
x^2 + x^2+34x+289 = 625
2x^2+34x+289 = 625
2x^2+34x-336 = 0
x^2+17x-168 = 0
(x+24)(x-7) = 0
x = {-24, 7}
throw out the negative solution (extraneous) leaving:
x = 7 meters (one leg)
.
second leg:
x+17 = 7+17 = 24 meters
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