A rectangular pen is built with one side against a barn. if 300 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen?

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

300-2w = length of the side parallel to the barn

A=w (300-2w)

A=-2w^2+300w

The formula for the w-value of maximum is:

=-b/2a

thus our value will be:

300/4

=75

and

300-2 (75)

=150

thus the dimensions to maximize the area is 75 by 150