Bubba, a farmer, wants to build a pen using the 20 ft 40 ft corner of his barn as part of the pen as shown in the figure below (the corner will not require any fencing). If Bubba has 124 ft of available fencing, then what will be the maximum area?
A) 2116 square feet
B) 1681 square feet
C) 1296 square feet
D) 961 square feet

Question

Bubba, a farmer, wants to build a pen using the 20 ft  40 ft corner of his barn as part of the pen as shown in the figure below (the corner will not require any fencing). If Bubba has 124 ft of available fencing, then what will be the maximum area? 
A) 2116 square feet 
B) 1681 square feet 
C) 1296 square feet 
D) 961 square feet

Quizplus · Accepted Answer

To maximize the area, we need to create a rectangle with sides parallel to the sides of the barn.
Let the length of the pen be x and the width be y. Then we have:
2x + y = 124 - 20 - 40 = 64
y = 64 - 2x
We want to maximize the area A = xy. Substituting for y, we get:
A = x(64 - 2x) = 64x - 2x^2
To find the maximum area, we can find the vertex of the parabola y = -2x^2 + 64x. The x-coordinate of the vertex is -b/2a = -64/(2(-2)) = 16. Substituting x = 16, we get y = 32. Therefore, the maximum area is A = 16 * 32 = 2116 square feet.

Bubba, a Farmer, Wants to Build a Pen Using the 20