Square for noobs

By the pythagorean theorem ,

$20^2=x^2+(x+y)^2$ $\color{#D61F06}\implies$ $400=x^2+x^2+2xy+y^2$ $\color{#D61F06}\implies$ $400=2x^2+2xy+y^2$ $\color{#3D99F6}\large (1)$

By the pythagorean theorem again,

$20^2=y^2+y^2$ $\color{#D61F06}\implies$ $400=2y^2$ $\color{#D61F06}\implies$ $200=y^2$ $\color{#3D99F6}\large (2)$

It follows that $y=\sqrt{200}\approx 14.142$

Substitute $\color{#3D99F6}\large (2)$ and $y \approx 14.142$ in $\color{#3D99F6}\large (1)$

$400=2x^2+2x(14.142)+200$ $\color{#D61F06}\implies$ $200=x^2+14.142x+100$ $\color{#D61F06}\implies$ $x^2+14.142x-100=0$

Using the quadratic formula to solve for $x$ , we get, $x=5.176$

Finally,

$x+y=5.176+14.142=$ $\boxed{19.32}$

Using Pythagoras theorem, we have $2y^2= 400\implies y^2=200 \implies y=14.142$ .

Also: $(x^2)+(x+y)^2= 400$ , substitute the value of $y$ in this equation and solve for $x$ , gives $x= 5.176 \implies s=19.32$ , where $s$ is the side of the square.