Are we allowed to answer this question? I asked since I noticed you were asking Greg himself.
And, you tagged this wrong. This question belongs to quant category.

In my humble opinion, this is not an issue of whether the triangle is equilateral or not; it is more about properties of “simliliar triangles”. In this picture, I don’t see why greg concluded it is an equilateral triangle either. But as long as we know these 3 trangles are simliar trangles, we don’t need to bother the angle.
As you assumed angle B and C are 50 degrees, it won’t affect the truth which BC:DE:FG=1:2:3, thus the ratio among the areas of three triangles (ABC ADE AFG) is 1:4:9 right? Thus, the answer to this question won’t change. 5:3 always stands regardless of whether ABC is equilateral triangle or not.