Let
be a triangle having
as lengths of its sides and let
be another triangle having
as lengths of its sides. If
are the areas of the two triangles, prove that
When does equality hold?
%V0
Let $T_1$ be a triangle having $a, b, c$ as lengths of its sides and let $T_2$ be another triangle having $u, v,w$ as lengths of its sides. If $P,Q$ are the areas of the two triangles, prove that
$$16PQ \leq a^2(-u^2 + v^2 + w^2) + b^2(u^2 - v^2 + w^2) + c^2(u^2 + v^2 - w^2).$$
When does equality hold?
Školjka