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Italian Mathematical Olympiad

Geometry Difficulty 4.3 AIME Find the answer Italy

A right parallelepiped has edges of length $a, b, c$ , with $a < b < c$ . If the length of one of the edges is increased by an amount $q$ , then the volume of the parallelepiped increases. In which of the following cases is the increase in volume maximum?

Pick one

Solution

Solution:

sides not increased. This product is clearly maximum when the two non-increased sides are $b$ and $c$ (the two longest), that is, when $a$ is increased.

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Source: MathNet, licensed CC-BY-4.0. Statement translated into English from it; metadata (topic, difficulty) added by this project.