The figure above consists of two equilateral triangles, one of which is inside the other. If the unshaded region within the larger triangle makes up 8/9 of that triangle's area, what is the ratio of the perimeter of the larger triangle to the perimeter of the smaller triangle?

Question

( The figure looks like a smaller triangle (shaded) inscribed in a bigger triangle ( unshaded)

Answer 1

1/9 of the larger triangle's area is unshaded. That means the linear (edge) dimension of the smaller shaded triangle is 1/3 of the edge dimension of the larger triangle. The perimeters of the two triangles will also be in a large:small = 3:1 ratio.