The parallelogram ABCD shows the points P and Q dividing each of the lines AD and DC in the ratio 1:4. What is the ratio in which R divides DB? What is the ratio in which R divides PQ?

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1 Answer
CW
May 5, 2018

see explanation.

Explanation:

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Let #|ABC|# denote area of #DeltaABC#
let #|ABCD|=10x, => |ABC|=|ADC|=|ABD|=|CDB|=(10x)/2=5x#
given #DQ:QC=1:4, => |ADQ|:|AQC|=|BDQ|:|BQC|=1:4#,
#=> |ADQ|=x, |AQC|=4x, and |BDQ|=x, |BQC|=4x#
given #AP:PD=1:4, => |AQP|:|PQD|=|ABP|:|PBD|=1:4#,
#=> |ABP|=x, |PBD|=4x#
and # |AQP|=1/5x, |PQD|=4/5x#
#|PDQB|=|PBD|+|BDQ|=4x+x=5x#
#=> |PQB|=|PDQB|-|PDQ|=5x-4/5x=21/5x#
#=> DR:RB=|PDQ|:|PQB|=4/5x:21/5x=4:21#

#PR:RQ=|BPD|:|BDQ|=4x:x=4:1#

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