Problem:
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
Answer Choices:
A. 776
B. 784
C. 798
D. 800
E. 812
Solution:
Let a,b, and c be the dimensions of the box. It is given that
140=4a+4b+4c and 21=a2+b2+c2​,
hence
35=a+b+c (1) and 441=a2+b2+c2 (2)
Square both sides of (1) and combine with (2) to obtain