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.

In Δ ACD , OP || CD

`∴ (AP)/(PD)=(AO)/(OC)`.......(1)  (BPT)

`In Δ Abc , OQ||AB`

`∴ (BQ)/(QC)=(AO)/(OC)`.......(2)  (BPT)

From (1) and (2), we get

`(AP)/(DP)=(BQ)/(QC)`

`(AP)/(18)=(35)/(15)`

`AP=(35xx18)/(5xx3)`

`AP=(7xx5xx3xx6)/(5xx3)`

`AP=(7xxcancel5xxcancel3xx6)/(cancel5xxcancel3)`

`AP = 42`

`AD=AP+PD`

`AD=42+18`

`AD=60`

Hence, the value of AD is  60 .