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If G is the centroid of $Δ A B C$ and $B C = 5, C A = 12, A B = 13$ then BG=

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a

$\frac{\sqrt{61}}{3}$

b

$\frac{\sqrt{13}}{3}$

c

$\frac{2 \sqrt{61}}{3}$

d

$\frac{\sqrt{26}}{3}$

answer is C.

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Detailed Solution

$a = 5, b = 12, c = 13 m e d i a n t h r o u g h B = \frac{1}{2} \sqrt{2 a^{2} + 2 c^{2} - b^{2}} = \frac{1}{2} \sqrt{2 (25 + 169) - 144} = \frac{1}{2} \sqrt{244} B G = \frac{2}{3} (\frac{1}{2} \sqrt{244}) = \frac{\sqrt{244}}{3} = \frac{2 \sqrt{61}}{3}$

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