2012 AMC 10B Problems/Problem 21

When you see a and 2a, you could think of 30-60-90 triangles. Since all of the other's lengths are a, you could think that b is root3a. Drawing the points out, it is possible to have a diagram where b=root3a. So, b=root3a, so B:A=root3a $\textbf{(A)}