# Algebra

Farmer Ed has
9,000 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?

1. 👍 1
2. 👎 0
3. 👁 3,317
1. x = length
y = width

x + 2 y = 9000 or x = 9000 - 2 y
A = x y
so
A = (9000-2y)y

2 y^2 - 9000 y = - A
y^2 - 4500 y = -A/2

y^2 - 4500 y +(4500/2)^2 = -A/2 + 5,062,500

(y-2250)^2 = -(1/2)(A-10,125,000)
so
width = 2250
length = 4500
area = 10,125,000 m^2

1. 👍 2
2. 👎 0

## Similar Questions

1. ### math

An ostrich farmer wants to enclose a rectangular area and then divide it into 4 pens with fencing parallel to one side of the rectangle. There are 720 feet of fencing available to complete the job. What is the largest possible

2. ### College Algebra

You have 800 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river,find the length and width of the plot that will maximize the area. What is the largest area that can

3. ### Math

A pig farmer wants to enclose a rectangular area and then divide it into three pens with fencing parallel to one side of the rectangle (see the figure below). There are 940 feet of fencing available to complete the job. What is

4. ### 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

1. ### calculus

If 800 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed? Answer to the nearest square foot without commas. For example, if the answer is 1,000, write

2. ### Calculus

A farmer has 1500 feet of fencing in his barn. He wishes to enclose a rectangular pen. Subdivided into two regions by a section of fence down the middle, parallel to one side of the rectangle. Express the area enclosed by the pen

3. ### math

A farmer has 90 meters of fencing and would like to use the fencing to create a rectangular garden where one of the sides of the garden is against the side of a barn. Let L represent the varying length of the rectangular garden

4. ### Calc

A rectangular page is to contain 30 sqaure inches of print. The margins on each side are 1 inch. Find the dimensions of the page sucha that the least amount of paper is used. A farmer plans to fence a rectangular pasture adjacent

1. ### Calculus 1

If you have 280 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?

2. ### math

A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed?

3. ### calculus help

Farmer Brown wants to fence in a rectangular plot in a large field, using a straight rock wall that is already there as the north boundary. The fencing for the east and west sides of the plot will cost \$3 a yard, but she needs to

4. ### Math

A farmer wishes to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. If the farmer can afford only 1600 yards of fencing, what