Ratio of areas to ratio of perimeters

I used the factor of multiplication k for similar figures. Since yellow:green is 3:1 that means large hexagon:small hexagon is 4:1. So $k^2 =4$ and thus the factor k = 2. Answer must be 2:1.

We denote the side length of the two hexagons be $x$ and $y$ as shown in my diagram. Since the they similar, we have

$\dfrac{x^2-y^2}{y^2}=\dfrac{3}{1}$

$x^2-y^2=3y^2$

$x^2=4y^2$

$x=2y$

Since they are similar, the ratio of their perimeters is also the ratio of their side lengths

$x=2y$

$\dfrac{x}{y}=\boxed{\dfrac{2}{1}}$