AD, BE and CF are the medians of the triangle ABC and G is centroid. If $A D = 15 c m$ , find $A G$ .

10

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Solution

The correct option is A 10
We know that centroid divides a median in the ratio $2 : 1$ .

So, $G$ divides $A D$ in the ratio $2 : 1$ .

Let $G D = x$ , then $A G = 2 x$ .

$∵ A D = A G + G D$

$∴ 15 = 2 x + x$

$\Rightarrow 3 x = 15$

$\Rightarrow x = \frac{15}{3} = 5 c m$

$\Rightarrow A G = 2 x = 2 \times 5 = 10 c m$

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