Question

A rectangular corral is enclosed using 120 m of fencing. The corral uses the side of a barn as one of its sides, so fencing is required on three sides of the rectangular region. What dimensions would maximize the area enclosed by the fence?

Answer 1

The dimensions would be 40 m by 40 m.

To maximize area and minimize perimeter we make the dimensions as close to equal as possible.  Since we only need fencing on 3 sides, 120/3 = 40; we can use 40 for each side.