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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. - Mathematics

Sum

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.

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Solution

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 .

Concept: Triangles Examples and Solutions
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RD Sharma Class 10 Maths
Chapter 7 Triangles
Q 14 | Page 126
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