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 ? 12None of the above2335

Solution

## The correct option is A 12ΔAPQ ~ 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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