A note on perfect dissections of an equilateral triangle

A perfect dissection of a polygon P into a polygon P ′ is a decomposition of P into internally disjoint pairwise incongruent polygons all similar to P ′. It is known that there is no perfect dissection of an equilateral triangle into smaller equilateral triangles. On the other hand, an equilateral triangle has trivial perfect dissections into any number n of right triangles where n ≥ 3. We give an example of a perfect dissection of an equilateral triangle into 7 non-right triangles and prove that 7 is the smallest number of tiles in such dissection.