Can't think of a clever problem name

Let's say this was possible:

Let $x^2$ , $y^2$ , and $z^2$ be the sides of the right triangle. Plugging them into $a^2 + b^2 = c^2$ , we have $x^4 + y^4 = z^4$ . By Fermat's Last Theorem , we know this must have no positive integer solutions $(x, y, z)$ , and thus there cannot exist a right triangle with perfect square sides.

Let us suppose that there can be a right-angled triangle with sides $a^2,b^2,c^2$

Then $a^4+b^4=c^4$ (Using Pythogoras Theorom) but according to Fermat's Last Theorem We know that there do not exist any Four Natural numbers such that $x^n+y^n=z^n$

So the Answer is $\huge\text{NOOOOOOOOOOOOOOOOOOOOOOOOOO}$