Question 42

G is the centroid of the equilateral triangle ABC, if AB = 9cm then AG is equal to

Solution

Side of equilateral triangle (a) = 9 cm

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

=> $$AD=\frac{9\sqrt{3}}{2}$$

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

=> AG : GD = 2 : 1

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

= $$\frac{2}{3} \times \frac{9\sqrt{3}}{2} = 3\sqrt{3}$$ cm

=> Ans - (A)

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