Finding the perimeter of a square

say $x$ is the side length of the square

by the pythagorean theorem

$x^2+x^2=\left(10\sqrt{2} \right)^2$

$2x^2=100(2)$

$2x^2=200$

$x^2=100$

$x=10$

Therefore, the perimeter is $4(10)=40$

Let $x$ be the length of the square. Then:

$2x^2=(10\sqrt{2})^2$ ............................ ${using\ the\ pythagorean\ theorm}$

$2x^2=200$ ............................................. $removing\ the \ square\ roots$

$x^2=100$ ............................................... $dividing\ by\ 2$

$x = 10$ ................................................... $that\ is\ the\ length\ of\ each\ side$

$So\ the\ perimeter\ is\ 40$