Answer
$35ft\times57ft$
Work Step by Step
Using Pythagorean Theorem, the other side length is given by
$\sqrt {(x+10)^2+x^2}$ and the know area is
$x\sqrt {(x+10)^2+x^2}=5000$
$2x^2+20x+100=\frac{25000000}{x^2}$
$2x^4+20x^3+100x^2-25000000=0$
Solving the equation numerically gives $x\approx57ft$
and the other side can be calculated as $35ft$