Question

a fence must be built to enclose a rectangular area of 20,000square feet. fencing material costs 3 per foot for the twosides facing north and south and 6 per foot for the other twosides. find the cost of the least expensive fence

Answer 1

A fence surrounding the field that is 200 feet long and 100 feet wide will cost $2400 to construct.

What is area?

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

Here,

Area of rectangle=20,000 square feet

Cost of building fence for north and south=$3 per feet

Cost of building fence for east and west=$6 per feet

Let the sides be x and y,

area=x*y

20000=xy

y=20000/x

Perimeter=2l+2b

=2(x+y)

Total cost will be,

=3*2x+6*2y

=6x+12y

C=6x+12*20000/x

C=6x+240000/x

dC/dx=6-240000/x²

dC/dx=0

6=240000/x²

6x²=240000

x²=40000

x=200 feet

y=100 feet

C=6*200+12*100

C=$2400

The cost of building a fence around the field of length 200 feet and width 100 feet is $2400.

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