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 \(AD\).

 

\(AD = \) \(cm\)