The square
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
has to be decomposed into
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
triangles (which are not overlapping) and which have all angles acute. Find the smallest integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
for which there exist a solution of that problem and for such
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
construct at least one decomposition. Answer whether it is possible to ask moreover that (at least) one of these triangles has the perimeter less than an arbitrarily given positive number.
%V0
The square $ABCD$ has to be decomposed into $n$ triangles (which are not overlapping) and which have all angles acute. Find the smallest integer $n$ for which there exist a solution of that problem and for such $n$ construct at least one decomposition. Answer whether it is possible to ask moreover that (at least) one of these triangles has the perimeter less than an arbitrarily given positive number.