[SPLIT] The sum of the lengths of two legs of a right triangle...

[okay]

Hello, I have another question which involves setting given information into a quadratic equation, and then solving. It reads: "The sum of the lengths of two legs of a right triangle is 34 meters. If the length of the hypotenuse is 26 meters, find the length of each leg."

What I get is x^2+34x=26^2, or x^2+34x-676=0. This appears incorrect to me, but I'm not sure how else I am supposed to apply the information given.

 

[HallsofIvy]

The Pythagorean Theorem says that \(\displaystyle a^2+ b^2= c^2\) where a and b are the lengths of the two legs, c the length of the hypotenuse. Saying that the "The sum of the lengths of two legs of a right triangle is 34 meters" means that a+ b= 34 or b= 34- a. So \(\displaystyle a^2+ b^2= a^2+ (34- a)^2= 26^2\). I don't know where you got "34x" (or 34a) in place of \(\displaystyle b^2\).