38. Exemplar exercise problems XI

$ABCD$ is a trapezium in which $AB||DC$ and $P$ and $Q$ are points on $AD$ and $BC$, respectively such that $PQ||DC$. If $PD = 18 \ cm$, $BQ = 35 \ cm$ and $QC = 15 \ cm$, find $AD$.

 

$AD =$ $cm$