A rancher has 200 feet of fencing.

Question

A rancher has 200 feet of fencing with which to enclose to adjacent rectangular areas. What dimensions should be used so that the enclosed area will be a maximum?

Answer 1

Well suppose length is x, and width is y

Then perimeter = 200, so 2x+2y = 200, so x + y = 100, so y = 100-x

Area = xy = x (100-x)

Plot this on Desmos or a TI-84 and choose x so this is a maximum

(obviously 0 < x < 100)