If a man is fencing in a rectangular lot of grass next to the road and doesnt want to fence the side touching the road and has 248 feet of fence, whats the maximum area he can fence?

Answer 1

If we use h and w for length and width, with length parallel to the road,

perimeter p = 2w+h = 248
Area = w*h = w(248-2w) = 248w - 2w^2

We want to maximize the area, so we take the derivative and set it to zero.

248-4w = 0
w = 62

So, h = 124

Maximum area = 62*124 = 7688 sq ft

For a given perimeter, a square has maximum area. Here, we use the road as one side, so we get to enclose two squares instead of one.