Track / Stage 4 / 113 of 340 #373 of 1964

Problem 373

AMC 12 late, AIME early

Geometry Difficulty 4.7 Find the answer

(2 points) Does there exist a rectangular parallelepiped with integer sides, for which the surface area is numerically equal to the sum of the lengths of all twelve edges?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Answer: Yes, it exists.

Solution: For example, a $2 \times 2 \times 2$ cube fits. Both the surface area and the sum of the lengths of the edges are 24.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.