Inscribing an equilateral triangle ABC into another equilateral triangle XYZ with AB $\perp$ YZ Equilateral $\Delta ABC$ is inscribed in equilateral $\Delta XYZ$ with $AB \perp YZ$. What is the ratio of the area of $\...--prophetes.ai

Inscribing an equilateral triangle ABC into another equilateral triangle XYZ with AB $\perp$ YZ Equilateral $\Delta ABC$ is inscribed in equilateral $\Delta XYZ$ with $AB \perp YZ$. What is the ratio of the area of $\Delta ABC$ to the area of $\Delta XYZ$?

![enter image description here](

The three external triangles are clearly congruent $1:\sqrt3:2$ right triangles, so the sides of the two equilateral triangles are in the ratio $\sqrt3:(2+1)=\sqrt3:3$. Therefore, the ratio of the two areas is $3:9 = 1:3$.