I watched computer monitors and I asked myself, do two monitors with the same display diagonal have the same display area?
I managed to find out that the answer is yes, if two right triangles with the same length hypotenuse have the same area. The answer is trivial if the two triangles are identical, and according to Thales' theorem I know that there are cases when two right triangles have the same length hypotenuse, but they are not identical (the legs length and the angles are different).
So my final question:
Do two, not identical right triangles with the same length hypotenuse have the same area?
I guess that the answer is yes, but I can't give a proof that I'm 100% sure.