Question

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

Answer 1

In trapezium ABCD, AB || DC. P and Q are points on sides AD and BC such that PQ || AB.

Join AC. Suppose AC intersects PQ in O.



$$\begin{gathered} \mathrm{In}∆ACD,OP\left|\right|CD \\ \therefore \frac{AP}{PD}=\frac{AO}{OC}.....\left(1\right)\left(\mathrm{BPT}\right) \\ \mathrm{In}∆ABC,OQ\left|\right|AB \\ \therefore \frac{BQ}{QC}=\frac{AO}{OC}.....\left(2\right)\left(\mathrm{BPT}\right) \end{gathered}$$

From (1) and (2), we get

Hence, the value of AD is .