KöMaL 2007 B4041

The lengths of the medians of a triangle are $a$, $b$, $c$. Prove that for all positive numbers $\alpha$, $\beta$, $\gamma$ it is possible to construct a triangle with sides $\alpha a$+$\beta b$+$\gamma c$, $\gamma a$+$\alpha b$+$\beta c$, $\beta a$+$\gamma b$+$\alpha c$.