2023 AMC 10B Problem 17

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 \frac{11}{2}, and the volume of \mathcal{P} is \frac{1}{2}. What is the length of the longest interior diagonal connecting two vertices of \mathcal{P}?

\textbf{(A)} 2 \qquad \textbf{(B)} \dfrac{3}{8} \qquad \textbf{(C)} \dfrac{9}{8} \qquad \textbf{(D)} \dfrac{9}{4} \qquad \textbf{(E)} \dfrac{3}{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.