# Math

A rectangular enclosure is to be constructed with 800 feet of fence in order to have four sections. What should be the dimensions in order to maximize the area enclosed? What is the maximum area?

1. Well, I bet it turns out to be a square but anyway:
A = b c where b is breadth and c is length

2 b + 2 c = 800
so
b + c = 400
c = (400 - b)
so
A = b * (400-b)
A = 400 b - b^2
b^2 - 400 b + A = 0
where is the vertex of this parabola (I assume you do not do calculus)
b^2 - 400 b = -A
b^2 - 400 b + 40,000 = -A + 40,000
(b-200)^2 = -A + 40,00
vertex (maximum) when b = 200
then c = 400-200 also = 200
just as we suspected

posted by Damon

## Similar Questions

1. ### College Algebra

A rectangular enclosure is to be constructed with 2,000 feet of fence in order to have four sections, as in the diagram below. What should be the dimensions in order to maximize the area enclosed? What is the maximum area? (So the
2. ### 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
3. ### Math

Please help with this problem! Brandon wishes to fence in a rectangular area of his lawn for his rabbit. If the measure, in feet, of each side of the enclosure is a positive integer and the perimeter of the enclosure is 70 feet,
4. ### math

2. You are installing a new pre-constructed fence in front of your house. Each fence section measures 4 1/2 feet wide, and each end will also have a decorative piece that measures 1 3/4 feet wide. If the space for the fence is 30
5. ### calculus

You have been hired by a farmer to design a fenced-in rectangular enclosure for emus. The emus will require 720 square feet of area in which to roam, and the fence will cost 20 dollars per foot. The rectangular area will adjoin an
6. ### PreCalculus

Three sides of a fence and an existing wall form a rectangular enclosure. The total length of a fence used for the three sides is 160 feet. Find the value(s) for which the area is 2800 square feet.
7. ### Algebra

Suppose a farmer has 120 feet of fencing to make a rectangular barnyard enclosure. If the enclosure is x feet long, express the area A of the enclosure as a function of the length x.
8. ### Math

Suppose a farmer has 120 feet of fencing to make a rectangular barnyard enclosure. If the enclosure is x feet long, express the area A of the enclosure as a function of the length x. Briefly explain.
9. ### Calculus

A home owner wants to fence in his yard of 600 sq. feet. Three sides are to be constructed with chain link fence at a cost of 3.25 per linear feet. The fourth side is to be constructed with a wood stockade fence at a cost of \$5.45
10. ### arithematic

A horticulturalist is building a fence around a rectangular garden using the side of the building for one side of the enclosure. she has 81 feet fencing. what should be the dimensions of the enclosure be so that she can maximize

More Similar Questions