You can put this solution on YOUR website!
I see three little kites in the corners of the triangle.
If you split one of them along the long diagonal, you get two congruent 30-60-90 right triangles.
The ratio of short leg to long leg in those triangles (and in all 30-60-90 right triangles) is
(It is usually written as
just for elegance, but it works better for me as
in this case).
That is the ratio of the side of the small square to the side of the medium square.
The ratio of their areas is the square of the ratio of their sides, or