Answer
$1250 \ ft^2$
Work Step by Step
Let us consider that $x$ and $y$ be the left boundary length and lower boundary length.
So, as per the given condition we can write as:
$8x+2y=400 \implies y=200-4x$
Further, to enclose the maximum area we must have: $\dfrac{dA}{dx}=0$
Also, $A=\dfrac{1}{2} xy=\dfrac{1}{2} x \times (200-4x)=\dfrac{200x-4x^2}{2}$
$\dfrac{dA}{dx}=0\\ \dfrac{200-8x}{2}=0 \implies x=25 \ ft$
and $y=200-100=100 \ ft$
Therefore, the required area is: $A=\dfrac{1}{2}(25)(100)=1250 \ ft^2$
