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ABCD is a trapezium in which ABabs()DC a...

ABCD is a trapezium in which AB`abs()`DC and P,Q are points on AD and BC respectively, such that PQ`abs()`DC, if PD=18 cm, BQ=35 cm and QC=15 cm. Find AD.

Text Solution

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Given: ABCD is a trapezium in which
AB||CD and
PQ ||DC (see figure)
Also, PD = 28 cm, BQ = 35 cm and QC = 15 cm
to find : AD
Proof: In trapezium ABCD,
AB || CD
PQ ||DC
AB||CD ||PQ …..(1)
in `triangleBCD` OQ||DC [ from (1)]
` (BO)/(OD) = (BQ)/(QC)` ( by BPT) ...(2)
similarly , in `triangleDAB`
PO||AB
`(BO)/(OD) = (AP)/(PD)` (by BPT ...(3)
from (2) and (3)
`(AP)/(PD) = (BQ)/(QC)`
`Rightarrow " " (AP)/28 = 35/15`
`Rightarrow AP = 35/25 xx 18 = 7xx6`
` AP = 35/15 xx 18 = 7xx6`
AP = 42 cm
AD= AP +PD= 42 cm + 18 cm = 60 cm
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