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 128 ft of available fencing, then what will be the maximum area?
A) 2209 square feet
B) 1764 square feet
C) 1369 square feet
D) 1024 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 128 ft of available fencing, then what will be the maximum area? 
A) 2209 square feet 
B) 1764 square feet 
C) 1369 square feet 
D) 1024 square feet

Quizplus · Accepted Answer

First, we will draw the diagram and label the sides of the pen.

Let x be the length of the side parallel to the barn and y be the length of the side perpendicular to the barn.

Since we know that there are 128 ft of fencing available, we can write an equation for the total length of fencing needed:

x + y + 40 + 20 = 128

Simplifying, we get:

x + y = 68

To maximize the area of the pen, we need to maximize the value of xy.

We can rewrite the equation for the total length of fencing as:

y = 68 - x

Substituting into the equation for area:

A = xy = x(68 - x) = 68x - x^2

To find the maximum area, we need to find the vertex of the parabola.

The x-coordinate of the vertex is:

x = -b/2a = -68/-2 = 34

Substituting back into the equation for area:

A = 68(34) - 34^2 = 2209

Therefore, the maximum area is 2209 square feet.

The best choice is A.

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