Gina has 3200 yards of fencing to enclose a rectangular area. find the dimensions of a rectangle that maximize the enclosed area. what is the maximum area?

Dimensions are 800 by 800

Area = 640,000

Step-by-step explanation:

Let the length be x and the width be y

The perimeter of a rectangle is give as ; 2 ( L + B) , that is

2(x+y) = 3200

divide through by 2 , we have

x + y = 3200/2

x + y = 1600

Making y the subject of formula , we have

y = 1600 - x

Let the are of the rectangle be A , then

A = xy

substitute the value of y into A , we have

A = x ( 1600 - x)

A = 1600x -

Since we are maximizing, we will find the derivative of A with respect to x , we have

= 1600 - 2x

set  to zero ,

1600 - 2x = 0

1600 = 2x

Therefore x =800

substitute the value of x = 800 into y , we have

y = 1600 - 800

y = 800

The dimensions are 800 by 800

The maximum area is therefore 800 x 800 = 640,000

16.9 times 2.85

step-by-step explanation: