SOLUTION: I have a world problem that I need help solving. Thank you. The hypotenuse of a right triangle is 26 ft long. One leg is 14 ft longer than the other. Find the length of the shorter

Question 190552: I have a world problem that I need help solving. Thank you. The hypotenuse of a right triangle is 26 ft long. One leg is 14 ft longer than the other. Find the length of the shorter leg.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
.
Let x = length of shorter leg
then
x+14 = length of longer leg
.
x^2 + (x+14)^2 = 26^2
x^2 + (x+14)(x+14) = 26^2
x^2 + x^2 + 28x + 196 = 676
2x^2 + 28x + 196 = 676
2x^2 + 28x - 480 = 0
x^2 + 14x - 240 = 0
(x+24)(x-10) = 0
x = {10, -24}
.
Toss out negative solution leaves us with
x = 10 feet

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