# SOLUTION: Hi all, I'm having trouble on this word problem. Hopefully someone can help me find the equation, this is tough. Thank you :) Find the length of the shorter leg of a right tri

Algebra ->  Equations -> SOLUTION: Hi all, I'm having trouble on this word problem. Hopefully someone can help me find the equation, this is tough. Thank you :) Find the length of the shorter leg of a right tri      Log On

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 Question 478232: Hi all, I'm having trouble on this word problem. Hopefully someone can help me find the equation, this is tough. Thank you :) Find the length of the shorter leg of a right triangle if the longer leg is 3 feet more than the shorter leg and the hypotenuse is 3 feet less than twice the shorter leg. The length of the shorter leg is ?? feetAnswer by nerdybill(7090)   (Show Source): You can put this solution on YOUR website!Find the length of the shorter leg of a right triangle if the longer leg is 3 feet more than the shorter leg and the hypotenuse is 3 feet less than twice the shorter leg. . Let s = length of short leg then from "longer leg is 3 feet more than the shorter leg ": s+3 = length of long leg and from "hypotenuse is 3 feet less than twice the shorter leg": 2s-3 = length of hypotenuse . Now we use Pythagorean theorem to get our equation: s^2 + (s+3)^2 = (2s-3)^2 s^2 + (s+3)(s+3) = (2s-3)(2s-3) s^2 + (s^2+6s+9) = (4s^2-12s+9) 2s^2+6s+9 = 4s^2-12s+9 6s+9 = 2s^2-12s+9 9 = 2s^2-18s+9 0 = 2s^2-18s 0 = s^2-9s 0 = s(s-9) s = {0, 9} throw out the zero case leaving: s = 9 feet