# area and perimeter

posted by .

a farmer wishes to build a fence around a rectangular field and divide it into two equal parts as well.the dividing fence must be parallel to one of the side of the field. you are asked to find dimension of the field of maximum area that you can fence and divide in two equal parts with a wire fence of 1200meter

• area and perimeter -

if the length is x and the width is y, then

2x+3y = 1200

a = xy = x(1200-2x)/3 = 400x - 2x^2/3
max area when x = 400*3/4 = 300

So, the field is 300 by 200

Note that as in all such problems, the fencing is divided equally among the lengths and widths.

• area and perimeter -

30000

## Similar Questions

1. ### shortest fence

this is my last question from applications of derivatives! A 216m^2 rectangular pea patch is to be enclosed by a fence and divided into two equal parts by another fence parallel to one of the sides. What dimensions for the outer rectangle …
2. ### math

A rectangular field is to be enclosed by a fence. Two fences parallel to one side of the field divide the field into three rectangular fields. If 2400m of fence are available find the dimensions giving the max area.
3. ### Calculus

A rancher wants to fence in an area of 500000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. What is the shortest length of fence that the rancher can use?
4. ### CALC

A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
5. ### Math

a farmer wants 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 only afford 1000 yards of fencing, what dimensions …
6. ### 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 dimensions …