Existence of the triangle with sides $\sqrt{bc}$, $\sqrt{ca}$, $\sqrt{ab}$.

Given the sides $a$,$b$,$c$ of a rectangle we would like to know if a triangle exists whose sides are $\sqrt{bc}$, $\sqrt{ca}$, $\sqrt{ab}$, the geometric means of $a$, $b$, $c$. 

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Existencia del triángulo con lados $\sqrt{bc}$, $\sqrt{ca}$, $\sqrt{ab}$