The centroid of a triangle $A B C$ is $8$ cm from the vertex $A$ . What is the length of the median of the triangle through $A$ ?

20

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16

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12

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10

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Solution

The correct option is C $12$ cm
The ratio of centroid to median of a triangle
$= 2 : 3$
$\Rightarrow \frac{l e n g t h o f c e n t r o i d}{l e n g t h o f m e d i a n} = \frac{2}{3}$
$\Rightarrow$ length of median $= \frac{3}{2} \times 8 c m$
$= 12 c m$

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