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 11 / 2, and the volume of \mathcal{P} is 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}