Answer: Side = \(5\sqrt{2}\) cm, perimeter = \(20\sqrt{2}\) cm
Let the side be x cm. The diagonal divides the square into two right-angled isosceles triangles, so by Pythagoras theorem
\[x^2 + x^2 = 10^2\] \[2x^2 = 100,\quad x^2 = 50\] \[x = \sqrt{50} = 5\sqrt{2}\] \[\text{Perimeter} = 4x = 20\sqrt{2}\ \text{cm}\]