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(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.

## Answer This Question

## Related Questions

- College Cal 1 - A farmer wants to fence off a rectangular field of area 15000 ...
- college Algebra - A rectangular fence is to be built along a river using the ...
- Pre-Calculas 11 - a farmer wants to build two pens (one for cows, the other for ...
- Math - Jennifer plans to fence a rectangular area around her rectangular ...
- 11th grade math - A farmer wants to fence in 60 000m^2 of land in a rectangular ...
- Math - 1. A gardener has 140 feet of fencing to fence in a rectangular vegetable...
- Calculus - A rancher wants to build a rectangular fence next to a river, using ...
- College Algebra - A farmer wants to build a rectangular fence using the side of ...
- Calc - A farmer wishes to enclose a rectangular pen with area 100 square feet ...
- Calc - A farmer wishes to enclose a rectangular pen with area 100 square feet ...

More Related Questions