Question

ABCD is a trapezium in which AB parallel CD and P,Q are the points on AD and BC respectively such that PQ parallel DC if PD is 18cm BQ is 35cm and QC is 15cm find AD​

Answer 1

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Construction: 

Join BD

In △ABD,  PO∥AB        [∵ PQ∥AB ]

⇒  DP/AP=DO/OB    [ By basic proportionality theorem ]          ------ ( 1 )

⇒  In △BDC, OQ∥DC    [ 

∵ PQ∥DC ]

BQ/QC=OB/OD    [ By basic proportionality theorem ]

⇒  QC/BQ=ODOB         ----- ( 2 )

⇒  DP/AP=QC/BQ       [ From ( 1 ) and ( 2 ) ]

⇒  18/AP=15/35

∴   AP=18×35/15=42

∴   AD=AP+DP=42+18=60cm

Answer 2

Step-by-step explanation:

Join BD

Apply basic proportionality theorem in the two triangles and equate the two equations so formed

.Find AP and then AD = 60cm