Multiple choice

The centroid of an equilateral triangle $ABC$ is $G$. If $AB$ is $6\ cms$, the length of $AG$ is

  1. $\sqrt {3} cm$
  2. $2\sqrt {3} cm$
  3. $3\sqrt {2} cm$
  4. $2\sqrt {2} cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In an equilateral triangle, the altitude h = (sqrt(3)/2) * side. Here, h = (sqrt(3)/2) * 6 = 3 * sqrt(3). The centroid divides the median in a 2:1 ratio, so AG = (2/3) * h = (2/3) * 3 * sqrt(3) = 2 * sqrt(3).

AI explanation

The median of an equilateral triangle is given by the formula altitude equals (side times the square root of 3) divided by 2. Substituting the side length of 6 cm gives an altitude of 3 times the square root of 3 cm. The centroid divides the median in a 2:1 ratio, meaning AG is two-thirds of the total altitude. Multiplying two-thirds by 3 times the square root of 3 yields a length of 2 times the square root of 3 cm.

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