Question

Pablo wants to build a rectangular pen for the pig he is raising in his agriculture class. Pablo only has 36 feet of fencing.

a. What representative function can be used to model the area of the rectangular pen as a function of the side length, x?
(A) A(x)=x^2
(B) A(x)=36−2x
(C) A(x)=18x−x^2
(D) A(x)=18−x

Answer 1

The function to model the area of the pig pen with 36 feet of fencing as a function of side length x is A(x)=18x-x^2.

Step-by-step explanation:

Pablo wants to build a rectangular pen for the pig he is raising and has 36 feet of fencing. The representative function that can be used to model the area of the rectangular pen as a function of the side length, x, is option (C) A(x)=18x-x^2. Here's why: if x represents one side of the rectangle, the adjacent side would be (36 - 2x) over 2, since there are two sides of length x and two of length (36 - 2x) over 2 to account for in the total fencing length. The area A, therefore, is the product of these sides, which simplifies to A(x)=18x-x^2.