A rectangular prism is being designed to have a volume of 36 cubic units. Find the minimum surface area in square units for the prism if the edge lengths are positive integers.
Since the edge lengths are integers, we start with the factors of 36:
36=2*2*3*3
and assemble take one or two factors to make a set of three numbers (out of 2,2,3,3) to represent edge lengths such that they are as close as possible. The cube so formed will have the minimum possible surface area.
I.e. : choose between
{(2,2,9), (2,3,6), (4,3,3)}
Calculate the surface area of each cube as a check.