ABCD is a trapezium in which AB // DC and P and Q are a point on AD and BC respectively suvh that PQ // DC . If PD = 18cm , BQ = 35cm and QC = 15cm , find AD
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Answer:
Construction: Join BD
In △ABD, PO∥AB [∵ PQ∥AB ]
⇒
AP
DP
=
OB
DO
[ By basic proportionality theorem ] ------ ( 1 )
⇒ In △BDC, OQ∥DC [
∵ PQ∥DC ]
QC
BQ
=
OD
OB
[ By basic proportionality theorem ]
⇒
BQ
QC
=
OB
OD
----- ( 2 )
⇒
AP
DP
=
BQ
QC
[ From ( 1 ) and ( 2 ) ]
⇒
AP
18
=
35
15
∴ AP=
15
18×35
=42
∴ AD=AP+DP=42+18=60cm
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