Problem:
A rectangular box has a total surface area of 94 square inches. The sum of the lengths of all its edges is 48 inches. What is the sum of the lengths in inches of all of its interior diagonals?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Denote the edge lengths by , and . The surface area is and the sum of the lengths of the edges is . Therefore , so . By the Pythagorean Theorem applied twice, each of the 4 internal diagonals has length , and their total length is . A right rectangular prism with edge lengths 3,4 , and 5 satisfies the conditions of the problem.
The problems on this page are the property of the MAA's American Mathematics Competitions