MathDB

69

Part of 1990 IMO Longlists

Problems(1)

Set of Cuboids - ILL 1990 PRK3

Source:

9/18/2010
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.
ratiogeometry proposedgeometry