Question 65

The length of diagonal BD of a parallelogram ABCD is 36 cm. P and Q are the centroids of triangle ABC and triangle ADC respectively. What is the length (in cm) of PQ?

Solution

Given : ABCD is a parallelogram and BD = 36 cm

To find : PQ = ?

Solution : The diagonals of a parallelogram bisect each other

=> BO = OD = $$\frac{36}{2}=18$$ cm

Also, a centroid intersects the median in the ratio 2 : 1

=> BP : PQ = 2 : 1

=> OP = $$\frac{1}{(1+2)}\times18=\frac{18}{3}=6$$ cm

Similarly, OQ = $$6$$ cm

$$\therefore$$ PQ = OP+OQ = $$6+6=12$$ cm

=> Ans - (C)

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