One leg of a right triangle is 24.0 cm longer than the other leg. If the hyptoenuse is to be greater than 65.0 cm, what values for the length of the other leg are permissible?

My work is:

$\displaystyle (25 + x)^2 + x^2 = 65^2$

$\displaystyle 625 + 50x + x^2 + x^2 = 65^2$

$\displaystyle 2x^2 + 50x - 3600 = 0$

$\displaystyle x = \frac{-50 \pm \sqrt{50^2 - 4(2)(-3600)}}{2(2)}$

$\displaystyle x = \frac{-50 \pm 176.92}{4}$

$\displaystyle x = 31.73\; or\; x = -56.73$

The $\displaystyle x = -56.73$ gets crossed out because its negative which leaves the $\displaystyle x = 31.73$ as the answer right? I don't think I right it just as $\displaystyle x = 31.73$ as the answer right?