Answer
$x=50~m$
$y=50~m$
$A=2500~m^2$
Work Step by Step
We need to find the vertex of $A=100x-x^2$
$A=-x^2+100x~~$ ($a=-1,b=100,c=0$):
$-\frac{b}{2a}=-\frac{100}{2(-1)}=50$
$f(50)=-50^2+100(50)=-2500+5000=2500$
Vertex: $(-\frac{b}{2a},f(-\frac{b}{2a}))=(50,2500)$
That is, when $x=50~m$ the maximum area is obtained ($A=2500~m^2$).
$y=100-x~$ (see item (b))
$y=100-50$
$y=50~m$
