Maths Olympiad Prep

Track / Stage 4 / 93 of 340 #353 of 1964

Problem 353

AMC 12 late, AIME early
Geometry Difficulty 4.7 Find the answer

1. (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?

A number or a short expression. Spacing and $ signs are ignored.

Official solution

Answer: Yes, it exists.

Solution: For example, a 2×2×22 \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 and solution reproduced as published; topic, difficulty and ordering added by this site.