Aaron has 144 identical cubes, each with edge length 1\:cm. He uses all of the cubes to construct a solid rectangular prism, which he places on a flat table. If the perimeter of the base of the prism is 20\:cm, what is the sum of all possible heights of the prism?
Answer Choices
A. 31\:cm
B. 25\:cm
C. 15\:cm
D. 22\:cm
E. 16\:cm