Let x represent the sides of the base of the square-based rectangular prism, and let h be the height of the prism.

We are told that the surface area is 2400 cm^2.

The equation we will use to define surface area will be

Solving for h, we get

Since , we can now substitute the expression we came up with into h:

Differentiate and then set equal to zero.

We take the positive value, since length can't be negative.

Now this implies that

Thus, the dimensions of the prism are

This prism is actually a cube.

Does this make sense?

--Chris