ABCD is trapezium in which AB||CD . P and Q are the mid points of AD and BC respectively such that PQ||CD. If AB= 8cm and CD= 10cm find the length of PQ. A B P R Q D C
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Step-by-step explanation:
Construction: Join BD
In △ABD, PO∥AB [∵ PQ∥AB ]
⇒ APDP=OBDO [ By basic proportionality theorem ] ------ ( 1 )
⇒ In △BDC, OQ∥DC [
∵ PQ∥DC ]
QCBQ=ODOB [ By basic proportionality theorem ]
⇒ BQQC=OBOD ----- ( 2 )
⇒ APDP=BQQC [ From ( 1 ) and ( 2 ) ]
⇒ AP18=3515
∴ AP=1518×35=42
∴ AD=AP+DP=42+18=60cm
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