Bubba, a farmer, wants to fence-in a three-sided area next to his barn, using the side of the barn as the fourth side of the rectangle. He also wants to divide this rectangular area into three identical pens (see figure below). If Bubba has 104 feet of available fencing, then each pen will have what dimensions in order to maximize its area? Round dimensions to nearest tenth.
A) 52 ft 26 ft
B) 26 ft 26 ft
C) 52 ft 13 ft
D) 26 ft 13 ft

Question

Bubba, a farmer, wants to fence-in a three-sided area next to his barn, using the side of the barn as the fourth side of the rectangle. He also wants to divide this rectangular area into three identical pens (see figure below). If Bubba has 104 feet of available fencing, then each pen will have what dimensions in order to maximize its area? Round dimensions to nearest tenth. 
A) 52 ft 26 ft 
B) 26 ft 26 ft 
C) 52 ft 13 ft 
D) 26 ft 13 ft

Quizplus · Accepted Answer

Let x be the length of one of the sides of the three pens. Then the perimeter of one pen is x+x+2x=4x. The perimeter of all three pens is 12x. Since Bubba has only 104 feet of fencing available, this means that 12x=104 or x=26.

Since one side of each pen is the barn, the rectangular area of each pen is 26*(104-2x)/3. Plugging in x=26, we get each pen has an area of 52*13=676 square feet.

To maximize the area, we want the pens to be as square as possible. Therefore, each pen has dimensions of 26 feet by 13 feet.

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