Problem:
A rectangular box P has distinct edge lengths a,b, and c. The sum of the lengths of all 12 edges of P is 13 the sum of the areas of all 6 faces of P is 11/2, and the volume of P is 1/2. What is the length of the longest interior diagonal connecting two vertices of P?
Answer Choices:
A. 2
B. 83
C. 89
D. 49
E. 23
Solution:
The longest diagonal passes through the interior of the box, connecting opposite vertices; its length is a2+b2+c2. Because 4a+4b+4c=13 and 2ab+2bc+2ac=211, it follows that