Afarmer wants to build a rectangular pen with 80 feet of fencing. the pen will be built against the wall of the barn, so one side of the rectangle won’t need a fence. what dimensions will maximize the area of the pen?

20 ft out from the wall by 40 ft parallel to the wall

Step-by-step explanation:

Let x represent the length of fence in the direction parallel to the wall. Then the other dimension of the rectangular pen is (80 -x)/2. The area is the product of these dimensions:

area = x(80 -x)/2

This function describes a downward-opening parabola with zeros at x=0 and x=80. The vertex (maximum) is halfway between the zeros, at x=40.

The dimensions are 40 ft parallel to the wall and 20 ft out from the wall.