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Question

In the given figure, P and Q are the mid-points of AC and AB. Also, PG = GR and HQ = HR. What is the ratio of area of ΔPQR : area of ΔABC ?

  1. 12
  2. None of the above
  3. 23
  4. 35


Solution

The correct option is A 12
ΔAPQ ~ ΔACB,BC=2PQ
and BC || PQ
AF = 2AE
AE = EF
Again ΔRGH ~ ΔRPQ
and PQ = 2GH
(By mid-point theorem)
RJ = 2RK
RK = JK
But since EF = JK
AE = EF = JK = RK
RJ = RK + JK  and  AF = AE + EF
and RJ = AF = h (say)
thenArea of ΔPQRArea of ΔABC=12×PQ×h12×BC×h=PQBC=12

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