Question 16
Let $ABCDE$ be a convex pentagon such that
$$
\begin{aligned}
& AB + BC + CD + DE + EA = 64 \text{ and } \\
& AC + CE + EB + BD + DA = 72.
\end{aligned}
$$
Compute the perimeter of the convex pentagon whose vertices are the midpoints of the sides of $ABCDE$.
$$
\begin{aligned}
& AB + BC + CD + DE + EA = 64 \text{ and } \\
& AC + CE + EB + BD + DA = 72.
\end{aligned}
$$
Compute the perimeter of the convex pentagon whose vertices are the midpoints of the sides of $ABCDE$.