what is wrong with following right triangle's hypotenuse's square reasoning

Question

In the image given in the link, the square of the hypotenuse is 2ab. But it can't be true. I can't be true. I can't seem to find the reason. any help would be appreciated.

Answer 1

Since you talk about hypotenuse, it means that the diagonals of the quadrilateral are perpendicular. Using $$c^2=a^2+b^2$$ and $$c^2=2ab$$ you get $$a^2+b^2-2ab=0$$ or $$(a-b)^2=0$$This is valid for $a=b$