A wire is cut into two pieces, one of length a and the other of length b. The piece of length a is bent to form an equilateral triangle, and the piece of length b is bent to form a regular hexagon. The triangle and the hexagon have equal area. What is \dfrac{a}{b} ?

**Answer Choices**

A. 1

B. \dfrac{\sqrt{6}}{2}

C. \sqrt{3}

D. 2

E. \dfrac{3 \sqrt{2}}{2}