SOLUTION: Find the length of the shorter side of a right triagle if the longer leg is 24 meters, and the hypotenuse is 6 more than twice the shorter leg.

Question 621160: Find the length of the shorter side of a right triagle if the longer leg is 24 meters, and the hypotenuse is 6 more than twice the shorter leg.

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Find the length of the shorter side of a right triagle if the longer leg is 24 meters, and the hypotenuse is 6 more than twice the shorter leg.
.
Let x = length of shorter leg
then
2x+6 = hypotenuse
.
applying the Pythagorean theorem:
x^2 + 24^2 = (2x+6)^2
x^2 + 576 = (2x+6)(2x+6)
x^2 + 576 = 4x^2+24x+36
576 = 3x^2+24x+36
0 = 3x^2+24x-540
dividing both sides by 3:
0 = x^2+8x-180
0 = (x+18)(x-10)
x = {-18,10}
throw out the negative solution leaving:
x = 10 meters (shorter side)

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