Answer
$$ l = 10+ \sqrt{52}, w= -10+ \sqrt{52}$$
Work Step by Step
We know:
$$ x(x+20)=1200$$
$$x^2+20x-1200=0$$
We solve:
$$ \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$
We find:
$$ \frac{-20 \pm \sqrt{20^2-4(1)(-1200)}}{2(1)}$$
This gives:
$$ l = 10+ \sqrt{52}, w= -10+ \sqrt{52}$$