Answer
$1250m^2$
Work Step by Step
The area is $x\cdot y=x(50-0.5x)=-0.5x^2+50x$ (from part a).
Let's compare $f(x)=-0.5x^2+50x$ to $f(x)=ax^2+bx+c$. We can see that a=-0.5, b=50, c=0. $a\lt0$, hence the graph opens down, hence its vertex is a maximum. The maximum value is at $x=-\frac{b}{2a}=-\frac{50}{2\cdot(-0.5)}=50.$ Hence the maximum value is $f(50)=-0.5(50)^2+50(50)=1250.$
