Posted by ryan on Wednesday, September 21, 2011 at 9:32pm.
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?

math  Steve, Thursday, September 22, 2011 at 5:11pm
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(2482w) = 248w  2w^2
We want to maximize the area, so we take the derivative and set it to zero.
2484w = 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.
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