Question

ABCD is trapezium if AB is parallel to CD P,Q are mid points of AD and BC such that PQ parallel to DC .PD=18cm BQ=35 cm and
QC=15cm find AD
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Answer 1

Answer:

Construction: Join BD

In △ABD, PO∥AB [∵ PQ∥AB ]

⇒ APDD = OBDO

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

⇒ In △BDC, OQ∥DC [

∵ PQ∥DC ]

QCBq

= ODOO [ By basic proportionality theorem ]

⇒ BQQC

= OBOO ----- ( 2

⇒ APDP = BQQQ [ From ( 1 ) and ( 2 ) ]

⇒ AP18 = 3515

∴ AP= 1518×35 =42

∴ AD=AP+DP=42+18=60cm