Answer
$100\ ft$ by $50\ ft$, maximum $ 5000\ ft^2$
Work Step by Step
Step 1. Assume the rectangle has dimensions of $x$ and $y$, where only one side is needed for $x$. We have $x+2y=200$ and $x=200-2y$
Step 2. The area of the rectangle is given by
$A=xy=y(200-2y)=-2y^2+200y$
Step 3. The maximum of the area can be found when
$y=-\frac{b}{2a}=-\frac{200}{-4}=50$
Thus $x=100$
Step 4. The dimensions should be $100\ ft$ by $50\ ft$ for a maximum area of $A=5000\ ft^2$
