ITMC 2018 Grade 8 National Preliminary set01 Question 6

$ABCD$ is a square and $O$ is the intersection of its diagonals. Triangle $PQR$ has base $QR=20$ cm. The ratio $[ABCD]:[PQR]$ is $8:5$, and $[AOB]=256$ cm². Find the height from $P$ in cm.