# Thread: Word Problem Using Triangle and System of Equations

1. ## Word Problem Using Triangle and System of Equations

I'm not sure if this should have been posted in geometry or not. I got this question in a precalculus class though. I received such wonderful help with the last question I figured I'd give this one a go as well. This is the last one for now...I promise =).

Solve the problem using systems of equations.
A right triangle has an area of 14 square inches. The square of the hypotenuse is 65. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.

2. Originally Posted by chipman316
I'm not sure if this should have been posted in geometry or not. I got this question in a precalculus class though. I received such wonderful help with the last question I figured I'd give this one a go as well. This is the last one for now...I promise =).

Solve the problem using systems of equations.
A right triangle has an area of 14 square inches. The square of the hypotenuse is 65. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.
$A = \frac{1}{2}ab$

$c^2 = a^2 + b^2$

We know that cē = 65 and A= 14

$14 = \frac{ab}{2}$ and $ab = 28$

$65 = a^2 + b^2$

and solve

3. thank you so much!