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

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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 ?? feet
Answer by nerdybill(7384) (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.
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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