AHSME 1996 Problem 23

The sum of the lengths of the twelve edges of a rectangular box is $140$, and the distance from one corner of the box to the farthest corner is $21$. The total surface area of the box is $\text{(A)}\ 776 \text{(B)}\ 784 \text{(C)}\ 798 \text{(D)}\ 800 \text{(E)}\ 812$