Question 7 (ii)
P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP. show that: (ii)ar(RQC)=38ar(ABC)
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Solution
CR is a median of ΔCAP, ⇒ar(ARC)=12ar(CAP)=12×12ar(ABC)=14ar(ABC) ------ (1)
Since RQ is median of ΔRBC, ar(ΔRQC)=12ar(ΔRBC) =12{ar(ΔABC)−ar(ΔARC)} =12{ar(ΔABC)−14ar(ΔABC)} =38ar(ΔABC)
Hence, ar(ΔRQC)=38ar(ΔABC)