ABCD is a trapezium in which AB||DC and P and Q are points on AD and BC respectively such that PQ||DC. If PD = 12 cm, BQ = 42 cm and QC = 18 cm, find AD.
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Step-by-step explanation:
Construction: Join BD
In △ABD, PO∥AB [∵ PQ∥AB ]
⇒
AP
DP
=
OB
DO
[ By basic proportionality theorem ] ------
⇒ 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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