Will give a farmer 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

Area is maximized and perimeter is minimized by using a figure that is as close to equilateral as possible.  Using the barn as one side of the pen, that means the farmer has 3 sides to fence.  300/3 = 100 feet for each side (this will make the figure equilateral).  This makes a square pen with dimensions 100 x 100.  This makes the area 10000 ft².