Problem:
The total area of all the faces of a rectangular solid is 22cm2, and the total length of all its edges is 24 cm. Then the length in cm of any one of its internal diagonals is
Answer Choices:
A. 11
B. 12
C. 13
D. 14
E. not uniquely determined
Solution:
With x,y,z,d as in the adjoining figure, we have
(1)2xy+2xz+2yz=22,
(2)4x+4y+4z=24,
(3)d2=x2+y2+z2.
From (2) we obtain (x+y+z)2=62, or
(4)x2+y2+z2+2xy+2xz+2yz=36.
Substituting (1) and (3) into (4) gives d2+22=36, or d=14. (Note: the dimensions of the solid are not uniquely determined, but d is!)
