Let $G$ be the centroid of $\triangle ABC$; that is, the point where the segments joining each vertex to the midpoint of the opposite side all meet.  If $\triangle ABG$ is equilateral with $AB=2$, then compute the perimeter of $\triangle ABC$.
Question:
Let $G$ be the centroid of $\triangle ABC$; that is, the point where the segments joining each vertex to the midpoint of the opposite side all meet.  If $\triangle ABG$ is equilateral with $AB=2$, then compute the perimeter of $\triangle ABC$.
Answer:
Let's think step by step.

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2+4\sqrt{7}
Let $G$ be the centroid of $\triangle ABC$; that is, the point where the segments joining each vertex to the midpoint of the opposite side all meet.  If $\triangle ABG$ is equilateral with $AB=2$, then compute the perimeter of $\triangle ABC$.
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