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Set of Cuboids - ILL 1990 PRK3

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September 18, 2010
ratiogeometry proposedgeometry

Problem Statement

Consider the set of cuboids: the three edges a,b,ca, b, c from a common vertex satisfy the condition ab=a2c5\frac ab = \frac{a^2}{c^5} (i) Prove that there are 100100 pairs of cuboids in this set with equal volumes in each pair.
(ii) For each pair of the above cuboids, find the ratio of the sum of their edges.
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