jmc

In rectangle $ABCD$, $P$ is a point on $BC$ so that $\angle APD=90^{\circ }$. $TS$ is perpendicular to $BC$ with $BP=PT$, as shown. $PD$ intersects $TS$ at $Q$. Point $R$ is on $CD$ such that $RA$ passes through $Q$. In $△PQA$, $PA=20$, $AQ=25$ and $QP=15$. Find the lengths of $BP$ and $QT$.

When writing your answer, first write the length of $BP$, then a comma, and then the length of $QT$. For example, if you find that these lengths are $5$ and $3/4$, respectively, your final answer should be written "5,3/4" (without the quotes).