A rectangular box \mathcal{P} has distinct edge lengths a, b, and c. The sum of the lengths of all 12 edges of \mathcal{P} is 13 , the sum of the areas of all 6 faces of \mathcal{P} is \dfrac{11}{2}, and the volume of \mathcal{P} is \dfrac{1}{2}. What is the length of the longest interior diagonal connecting two vertices of \mathcal{P}?
Answer Choices
A. 2
B. \dfrac{3}{8}
C. \dfrac{9}{8}
D. \dfrac{9}{4}
E. \dfrac{3}{2}