# Right Triangle problem

• December 15th 2012, 06:27 PM
mathematics123
Right Triangle problem
Hi, I've been working on this problem for a while now and can't seem to figure it out. I know the right answer but I'm having problems getting to it on my own.

Here's the problem: "Find the length of the shorter leg of a right triangle if the longer leg is 3cm more than the shorter leg and the hypotenuse is 6cm more than the shorter leg."

Here is the what I have so far, I know the answer is 9cm but I cannot figure out how they got to that.

Shorter leg = x, longer leg = x+3, hypotenuse = x+6. Using a2 + b2 = c2 I get x2 + (x+3)2 = (x+6)2

x2 + x2 + 9 = x2 + 36

2x2 + 9 = x2 + 36
-9 - 9
2x2 = x2 + 27
-x2 -x2

x2 = 27 ??????
• December 15th 2012, 06:46 PM
jakncoke
Re: Right Triangle problem
You are correct until the $x^2 + (x+3)^2 = (x+6)^2$ I think maybe you distributed wrong. $(x+6)^2 \not = x^2 + 6^2$

Here, $(x + 6)^2 = (x+6) * (x+6) = x*x + x*6 + 6*x + 6*6 = x^2 + 12x + 36$
$(x+3)^2 = (x+3)*(x+3) = x*x + x*3 + 3*x + 3*3 = x^2 + 6x + 9$
• December 15th 2012, 07:08 PM
mathematics123
Re: Right Triangle problem
Thank you very much!! I knew that too, I can't believe I did that.