ILL 1990 Problem 69

Consider the set of cuboids: the three edges $a, b, c$ from a common vertex satisfy the condition $$\frac ab = \frac{a^2}{c^5}$$ (i) Prove that there are $100$ 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.