Afarmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. the barn itself will be used as one of the sides of the enclosed area. what is the maximum area that can be enclosed by the fencing? enter your answer in the box. ft²

Let x represent the length of the side of the pen that is parallel to the barn. Then the area (y) will be
.. y = x(300 -x)/2
This describes a downward opening parabola with zeros at x=0 and x=300. The vertex (maximum) will be found at the value of x that is halfway between those, x = 150.

For that value of x, the pen area is
.. y = 150(300 -150)/2 = 150^2/2 = 11,250 . . . . . square feet.