jmc

Drawing the diagonal of a square divides the square into two 45-45-90 triangles. The diagonal is the hypotenuse of both triangles, and each leg of each triangle is a side of the square. Since the hypotenuse of a 45-45-90 triangle is $\sqrt{2}$ times the length of each leg, the length of the diagonal of the square is $$50\sqrt{2}\cdot \sqrt{2}=50{\left(\sqrt{2}\right)}^2=50\cdot 2=\boxed{100}.$$