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's call the length of each of the three pens "x."

Since we have 104 feet of fencing available, we can set up the equation:

2x + 2(2x) = 104

This simplifies to:

6x = 104

x = 17.33

However, the question asks us to round to the nearest tenth, so x ≈ 17.3.

Each pen is a rectangle with a length of 2x (since there are two of them) and a width of x. Plugging in x ≈ 17.3, we get:

Length = 2x ≈ 34.7
Width = x ≈ 17.3

So the dimensions of each pen are approximately 34.7 feet by 17.3 feet, making the answer C the best choice.

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