Question

Can a right triangle be equilateral?

Answer 1

The answer is no.
As we know, the Pythagorean theorem states the relation between sides of the right triangle:
a^2+b^2=c^2
Let's imagine that we have equilateral right triangle. So all three sides of it are equal, let's denote them by x.
So we have
x^2+x^2=x^2
or 2x^2=x^2 this equation holds only for x=0.
Therefore there cannot be equilateral right triangle.