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Let a, b, c be the edges.

$\begin{cases}ab = 3\\bc = 2\sqrt 3\\ca = \sqrt{15}\end{cases}$

(1) * (3) / (2) : 

$a^2 = \dfrac{3\sqrt{15}}{2\sqrt 3} = \dfrac{3\sqrt 5}2\\ a = \sqrt{\dfrac{3\sqrt 5}2}$

Similarly, 

$b = \sqrt{\dfrac6{5}\sqrt5}$ and $c = \sqrt{2\sqrt 5}$

Required ratio = b : c = $\sqrt 3 : \sqrt 5$