A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?

since the total amount of wire is not given, I looked for a similar question:

since we need to only calculate 3 sides of the land plot, our perimeter will be:

L + 2W = 800

area = L x W

L = 800 - 2W

now we replace:

area = (800 - 2W) x W = 800W - W²

we can write a quadratic equation:

area = -W² + 800W

the vertix of W = -b/2a

the coefficients of our quadratic equation are: -2 and 8

the vertix of W = -800 / (2 x -2) = -800 / -4 = 200 yards

width = 200 yards

length = 800 - (200 x 2) = 400 yards

maximum area enclosed = 200 x 400 = 80,000 sq yards