Question 87
Let $ABCD$ be a parallelogram such that $\measuredangle BAD \lt 90^\circ$ and let $DE$, $E \in AB$, and $DF$, $F \in BC$, be the altitudes of the parallelogram. Prove that
$$
4(AB \cdot BC \cdot EF + BD \cdot AE \cdot FC) \leq 5 \cdot AB \cdot BC \cdot BD
$$
Find $\measuredangle BAD$ if the equality occurs.
$$
4(AB \cdot BC \cdot EF + BD \cdot AE \cdot FC) \leq 5 \cdot AB \cdot BC \cdot BD
$$
Find $\measuredangle BAD$ if the equality occurs.