Expert: Azeem Hussain - 5/7/2009

Question
I read your answer to another student about how to solve a question similar to this one:
"The hypotenuse of a triangle is 15 feet long. The longer of the two legs is three feet longer than the other. Find the length of the shorter leg."
Now here is what I have done. I have already given values to a,b and c. They are "x", "x+2" and 15^2 in that order. So I have in front of me:
15^2=x^2+(x+2)^2
But what I don't know is how to go from there... how do I use the quadratic formula to solve for "a" and "b".

Thankyou,
Tim

Answer
Hi Tim,

Start by expanding your squares.
15²=x²+(x+2)²
(15)(15)=x²+(x+2)(x+2)
225=x²+x²+2x+2x+4

Collect like terms.
225=2x²+4x+4

Bring all the terms to one side of the equation, so that the other equals 0.
0=2x²+4x-221

At this point, you have 2, 4, and -221 as your a, b, and c values respectively.

Glad to help,
Azeem