Baltic Way 2023 · Problem 9

Answer: Yes, there is. Choose an arbitrary positive integer $m$ and draw a height in the right triangle with ratio of legs $1 : m$. This height cuts the triangle in two similar triangles with similarity coefficient $m$. The largest of them can further be cut into $m^2$ smaller equal triangles by splitting all sides in $m$ equal parts and connecting corresponding points with parallel lines. Thus a triangle can be split into $m^2 + 1$ equal triangles.

The figure shows this for $m = 4$, but in our problem we must take $m = 10$.