Question 52

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

Solution

Side of equilateral triangle (a) = 6 cm

Median AD of equilateral triangle = $$\frac{\sqrt{3}a}{2}$$

=> $$AD=\frac{6\sqrt{3}}{2}$$ cm

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

=> AG : GD = 2 : 1

$$\therefore AG = \frac{2}{3} \times AD$$

= $$\frac{2}{3} \times \frac{6\sqrt{3}}{2} = 2\sqrt{3}$$ cm

=> Ans - (B)

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