Question

What are the dimensions to maximize the area of a rectangular horse pen with 200 feet of fencing if the north side of the pen uses the side of the barn?

Answer 1

The dimensions to maximize the area is 50 by 100

Explanation:

Let x= the length of the side perpendicular to the barn

and 200-2x= length of the side parallel to the barn

Area = x(200-2x) (1)

Area =-
`x^(2)`+200x

The formula for the w-value of maximum is: -b/2a

thus our value will be:

200/4 =50

and substitue x = 50 into (1), we have: 200-2(20) =100

Thus the dimensions to maximize the area is 50 by 100