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. The final diagram looks something like this: .---b---. a 2a a . a .

 a   a
    .

So, b=root3a, so B:A=root3a=(A)