IMO 1970 LL GDR31

Prove that for any triangle with sides a, b, c and area P the

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IMO 1970 LL GDR31

Origin: GDR

Problem

Prove that for any triangle with sides a, b, c and area P the following inequality holds: P \leq \sqrt 4 (abc)2/3. Find all triangles for which equality holds.