ABCD is a trapezium in which AB || CD and P and Q are points on AD and

1.	ABCD is a trapezium in which AB \|\| CD and P and Q are points on AD and BC respectively, such that PQ \|\| DC. IfPD = 18 cm, BQ = 35 cm and QC = 15 cm, find AD.
Answer» 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

ABCD is a trapezium in which AB || CD and P and Q are points on AD and BC respectively, such that PQ || DC. IfPD = 18 cm, BQ = 35 cm and QC = 15 cm, find AD.

Answer»

ANSWER:

CONSTRUCTION: JOIN BD

In △ABD, PO∥AB [∵ PQ∥AB ]

⇒

[ By basic proportionality theorem ] ------ ( 1 )

⇒ In △BDC, OQ∥DC [

∵ PQ∥DC ]

[ By basic proportionality theorem ]

⇒

----- ( 2 )

⇒

[ From ( 1 ) and ( 2 ) ]

⇒

∴ AP=

18×35

=42

∴ AD=AP+DP=42+18=60cm

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ABCD is a trapezium in which AB || CD and P and Q are points on AD and BC respectively, such that PQ || DC. IfPD = 18 cm, BQ = 35 cm and QC = 15 cm, find AD.​

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ABCD is a trapezium in which AB || CD and P and Q are points on AD and BC respectively, such that PQ || DC. IfPD = 18 cm, BQ = 35 cm and QC = 15 cm, find AD.