an open rectangular box with a volume of 12 ft^3 has a square base. Express the surface area A of the box as a function of the length x of a side...

Hello!

I suppose that "open" means "without the upper side" and that `x` is in feet.

Denote the height as `h` (ft). Then the surface area is `A=x^2+4hx` (bottom square `x` by `x` and 4 sides `x` by `h`), and the volume is `x^2 h=12,` so `h=12/x^2.`

Then `A=A(x)=x^2+48/x` `(ft^2).` This is the answer.