Multiple choice

If G is the centroid and AD be a median with length $12$ cm of $\Delta ABC$, then the value of AG is

  1. $4$ cm
  2. $8$cm
  3. $10$ cm
  4. $6$ cm
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B Correct answer
Explanation

The centroid G of a triangle divides the median AD in the ratio 2:1. Given AD = 12 cm, AG = (2/3) * AD = (2/3) * 12 = 8 cm.

AI explanation

The centroid of a triangle divides each median in the ratio of 2 to 1, measured from the vertex to the midpoint of the opposite side. Since AD is a median with a total length of 12 cm, the distance from vertex A to the centroid G is two-thirds of the median. Calculating two-thirds of 12 cm gives AG = 8 cm.

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