Question 130
Let $ABCD$ be a square with side length $3~\mathrm{cm}$. The points $M$, $N$ and $P$ lie on the sides $(AB)$, $(BC)$ and $(CD)$, respectively, such that the quadrilateral $AMNP$ is a trapezoid with bases $MN$ and $AP$, having perpendicular diagonals, and $BN=1~\mathrm{cm}$. Compute the perimeter of the trapezoid $AMNP$.