15. A string is divided into two segments of lengths $a$ and $b$. The segments of lengths $a$ and $b$ are used to form an equilateral triangle and a regular hexagon, respectively. If their areas are equal, then $\frac{a}{b}=$ ( ).
(A) 1
(B) $\frac{\sqrt{6}}{2}$
(C) $\sqrt{3}$
(D) 2
(E) $\frac{3 \sqrt{2}}{2}$
15. B.
$$
\begin{array}{l}
\frac{\sqrt{3}}{4}\left(\frac{a}{3}\right)^{2}=\frac{3 \sqrt{3}}{2}\left(\frac{b}{6}\right)^{2} \\
\Rightarrow \frac{a^{2}}{9}=\frac{b^{2}}{6} \Rightarrow \frac{a}{b}=\frac{\sqrt{6}}{2} .
\end{array}
$$