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]$latex \frac{20\sqrt{3}}{3}cm&s=1$
[B]$latex 10\sqrt{3}cm$
[C]$latex \frac{10\sqrt{3}}{3}cm&s=1$
[D]$latex 5\sqrt{3}cm$

$latex \mathbf{\frac{10\sqrt{3}}{3}cm}&s=1$
AB = 10cm
BD = 5 cm
∠ADB = 90°
∴ AD = $latex \sqrt{AB^{2} – BD^{2}}$
$latex => \sqrt{10^{2}-5^{2}} = \sqrt{100-25}$
$latex => \sqrt{75} = 5\sqrt{3}cm$
$latex AG =$ $latex \frac{2}{3}&s=1$ $latex AD=$ $latex \frac{2}{3}\times 5\sqrt{3}&s=1$
$latex = \frac{10\sqrt{3}}{3}cm&s=1$
Hence option [C] is the right answer.


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