math
posted by ryan .
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
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.
Respond to this Question
Similar Questions

College Algebra
A farmer wants to build a rectangular fence using the side of his barn as one side. He has 200 yards of fencing available. Find the maximum possible area he can enclose with the fence. 
Math
Jennifer plans to fence a rectangular area around her rectangular swimming pool. The total area enclosed by the fence, including the pool, should be 5 times the area of the pool alone. The pool is 20 feet by 17 feet. A.)What is the … 
PreCalculas 11
a farmer wants to build two pens (one for cows, the other for horses) on land by a straight road. There is already a fence along the road and the farmer has 800m of fencing to build his fence to enclose the pens and separate them as … 
Calculus
A rancher wants to build a rectangular fence next to a river, using 100 yd of fencing. What dimensions of the rectangle will maximize the area? 
College Cal 1
A farmer wants to fence off a rectangular field of area 15000 square feet using barbed wire fencing. SInce the opposite of the road is a cornfield, he wants a twostrand fence along the road, and one strand on each of the other three … 
college Algebra
A rectangular fence is to be built along a river using the river as one side of the fence.the cost of the fencing for the two ends is $8 per sq ft and the cost of the fencing for the side running parallel to the river is $12 per sq … 
Math
1. A gardener has 140 feet of fencing to fence in a rectangular vegetable garden. Find the dimensions of the largest area he can fence. Find the possible rectangular area he can enclose. 2. Suppose a farmer has a large piece of land … 
Math
Tiffany is constructing a fence around a rectangular tennis court. She must use 300 feet of fencing. The fence must enclose all four sides of the court. Regulation states that the length of the fence enclosure must be at least 80 feet … 
Calculus
A fence must be built in a large field to enclose a rectangular area of 25,600m^2. One side of the area is bounded by n existing fence, so no fence is needed for that side. Materials for the fence cost $3 per meter for the two ends … 
math
3) You are fencing a rectangular puppy kennel with 25 ft of fence. The side of the kennel against your house does not need a fence. This side is 9 ft long. Find the dimensions of the kennel. 4) A gardener is planning a rectangular …