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.