Question
In an equilateral triangle ABC, G is the centroid. Each side of the triangle is 6 cm. The length of AG is:
Answer: Option C
In Equilateral triangle
$$\eqalign{
& AG:GD = 2:1 \cr
& AD = \frac{{\sqrt 3 }}{2}a \cr
& AD = \frac{{\sqrt 3 }}{2} \times 6 \cr
& AD = 3\sqrt 3 \cr
& 3 \to 3\sqrt 3 \cr
& 1 \to \sqrt 3 \cr
& AG = 2\,{\text{unit}} = 2\sqrt 3 \,{\text{cm}} \cr} $$
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In Equilateral triangle
$$\eqalign{
& AG:GD = 2:1 \cr
& AD = \frac{{\sqrt 3 }}{2}a \cr
& AD = \frac{{\sqrt 3 }}{2} \times 6 \cr
& AD = 3\sqrt 3 \cr
& 3 \to 3\sqrt 3 \cr
& 1 \to \sqrt 3 \cr
& AG = 2\,{\text{unit}} = 2\sqrt 3 \,{\text{cm}} \cr} $$
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