Answer
The width and the length are $50$
Work Step by Step
Let $x$ be the width, then the length is $100-x$, then the area is: $x(100-x)=-x^2+100x$
Let's compare $f(x)=-x^2+100x$ to $f(x)=ax^2+bx+c$. We can see that a=-1, b=100, c=0. $a\lt0$, hence the graph opens down, hence its vertex is a maximum. The maximum value is at $x=-\frac{b}{2a}=-\frac{100}{2\cdot(-1)}=50.$ Hence the width and the length are $50$.
