Question 13
Each face of two noncongruent parallelepipeds is a rhombus whose diagonals have lengths $\sqrt{21}$ and $\sqrt{31}.$ The ratio of the volume of the larger of the two polyhedra to the volume of the smaller is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$ A parallelepiped is a solid with six parallelogram faces such as the one shown below.
