The volume of a rectangular prism with a square base is fixed at 120 cubic feet.

Write the surface area of the prism as a function Ax) of the length of the side of the square x-

a. A (x) = x/480 + 2x^2

b. A (x) = 240/x + 2x^2

c. A (x) = 480/x + 2x^2

d. A (x) = 480/x + 2x^3

The correct answer is C. A (x) = 480/x + 2x²

Step-by-step explanation:

1. Let's review the information given to us to answer the problem correctly:

Volume of a rectangular prism with square base = 120 cubic feet

Side of the square base = x

Height of the prism = h

2. Write the surface area of the prism as a function A (x) of the length of the side of the square x.

Let's find out A (x) this way:

Volume of a rectangular prism with square base = 120 cubic feet

x² * h = 120

h = 120/x²

Now, let's substitute h in the surface area formula, this way:

Surface area = 2 * side of the square base² + 4 * side of the square base * height

A (x) = 2x² + 4x * 120/x² (Recall 120/x² = h and side of the square = x)

A (x) = 2x² + 480x/x²

A (x) = 2x² + 480/x

The correct answer is C. A (x) = 480/x + 2x²