Answer
$250 \ ft^2$
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:
$5x+y=100 \implies y=100-5x$
Further, to enclose the maximum area we must have: $\dfrac{dA}{dx}=0$
Also, $A=\dfrac{1}{2} xy=\dfrac{1}{2} x \times (100-5x)=\dfrac{100-10x}{2}$
$\dfrac{100-10x}{2}=0 \implies x=10 \ ft$ and $y=100-(5)(10)=50 \ ft$
Therefore, the required area is: $A=\dfrac{1}{2}(10)(50)=250 \ ft^2$
