Multiple choice

The length of the diagonal BD of the parallelogram ABCD is 18 cm. If P and Q are the centroids of ∆ADC and ∆ABC respectively then the length of PQ is?

  1. 9 cm

  2. 5 cm

  3. 8 cm

  4. 6 cm
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D Correct answer
Explanation

In a parallelogram, the centroid of a triangle divides the median in a 2:1 ratio. The distance between centroids of two triangles sharing a diagonal is 1/3 of the diagonal length. PQ = (1/3) * BD = 18 / 3 = 6 cm.

AI explanation

The centroids of triangles ADC and ABC divide the median from C to diagonal BD in a 2:1 ratio. Because both centroids lie on this same median, the distance between them represents one-third of the total diagonal length BD. Calculating one-third of the 18 cm diagonal gives a length of 6 cm for PQ.

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