## Precalculus (6th Edition) Blitzer

$200x-\frac{3}{2}x^2$
Step 1. The total length of the fence is the sum of the perimeter of the large rectangle and the middle fence, we have $2(l+w)+w=400$ or $2l+3w=400$, thus $l=\frac{1}{2}(400-3w)$. Since $w=x$, we have $l=\frac{1}{2}(400-3x)\ ft$ Step 2. The area is given by $A=lw=\frac{1}{2}(400-3x)x=200x-\frac{3}{2}x^2\ ft^2$