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Geometry Difficulty 4.3 AIME Find the answer Italy

A right parallelepiped has edges of length a,b,ca, b, c, with a<b<ca < b < c. If the length of one of the edges is increased by an amount qq, 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 bb and cc (the two longest), that is, when aa 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.