\textbf{147.} A triangle has side lengths $13$, $14$, and $15$. What is the side length of the regular hexagon circumscribed about this triangle?
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(1) $8$ \hfill (2) $\dfrac{8\sqrt{3}}{3}$ \hfill (3) $4$ \hfill (4) $\dfrac{4\sqrt{3}}{3}$
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