G is the centroid in the equilateral △ ABC. If AB = 10 cm then length of AG is :

G is the centroid in the equilateral △ ABC. If AB = 10 cm then length of AG is :
[A]\frac{20\sqrt{3}}{3}cm
[B]10\sqrt{3}cm
[C]\frac{10\sqrt{3}}{3}cm
[D]5\sqrt{3}cm

\mathbf{\frac{10\sqrt{3}}{3}cm}
AB = 10cm
BD = 5 cm
∠ADB = 90°
∴ AD = \sqrt{AB^{2} - BD^{2}}
=> \sqrt{10^{2}-5^{2}} = \sqrt{100-25}
=> \sqrt{75} = 5\sqrt{3}cm
AG = \frac{2}{3} AD= \frac{2}{3}\times 5\sqrt{3}
= \frac{10\sqrt{3}}{3}cm
Hence option [C] is the right answer.

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