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Q)

In a parallelogram ABCD,P divides AB in the ratio 2:5 and Q divides DC in t

In a parallelogram ABCD,P divides AB in the ratio 2:5 and Q divides DC in the ratio 3:2.If AC and PQ intersect at R,find the ratios AR:RC and PR:RQ

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A)

AK∣∣PQ and PQ||LC

AO=h (height)

APR and CQR similar triangles AR/RC=PR/RQ

AP=2*X

 PB=5*X

DQ=3*Y

QC=2*Y

 2*X+5*X=3*Y+2*y

 X/Y=5/7

Area APQK=2*X*h

 Area PLCQ=2*Y*h

AreaAPQK/AreaPLCQ=AR/RC=PR/RQ=(2*X*h)/(2*Y*h)=X/Y=5/7

 

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