In $\Delta ABC,$ $D$ is the midpoint of $BC$ and $G$ is the centroid of the triangle. If $GD = 2 \ cm,$ then the length of $AD$ is:

The centroid of a triangle divides any median in the ratio of 2 to 1, measuring from the vertex to the midpoint of the opposite side. Given that D is the midpoint of BC, AD is a median, and G is the centroid that splits AD into two parts: AG and GD. Since GD is the smaller part representing 1 unit of the ratio and equals 2 cm, the total length of median AD is 3 times 2 cm, which is 6 cm.

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