Question 142
Let $ABC$ be an acute triangle and let $MNPQ$ be a square inscribed in the triangle such that $M, N \in BC$, $P \in AC$, $Q \in AB$. Prove that
$$
\operatorname{area}[MNPQ] \leq \frac{1}{2} \operatorname{area}[ABC]
$$
$$
\operatorname{area}[MNPQ] \leq \frac{1}{2} \operatorname{area}[ABC]
$$