check the first picture below.
bearing in mind that, the river side doesn't get any fencing, because the river itself is acting as a fence, then the 300 feet will be only for those two widths there and the length.
[tex]\bf A=width\cdot length\implies A(w)=w~\stackrel{length}{(~300-2w)}
\\\\\\
A(w)=300w-2w^2\implies \cfrac{dA}{dw}=300-4w\implies 0=300-4w
\\\\\\
4w=300\implies w=\cfrac{300}{4}\implies w=75[/tex]
now, doing a first-derivative test on the regions before and after the critical point of 75, check the second picture below, 75 is clearly a maximum.
so, the largest Areas is at A(75) = 11250.
