5. We will call a right-angled triangle elegant if one of its legs is 10 times longer than the other. Is it possible to cut a square into 2020 identical elegant triangles?
Answer: Yes

Solution. An elegant triangle with legs of 10 and 100 can be cut into 100 triangles with legs of 1 and 10 (the cuts are straight lines parallel to its sides). From four such large triangles, we can form a square (its sides will be the hypotenuses of these triangles) with a hole (in the shape of a square with side $100-10=90$). This square can be divided into rectangles with sides 1 and 10 (there will be 810 such rectangles), and each such rectangle can be divided into two triangles with legs of 1 and 10. In total, we get $4 \cdot 100 + 2 \cdot 810 = 2020$ elegant triangles.

Grading. Full solution - 7 points.