The perimeter of the triangle formed by  $(0,0),(1,0)$ and  $(0,1)$ is

$A(0,0),B(1,0)$ and  $C(0,1)$

$AB=\sqrt{{(1-0)}^2+{(0-0)}^2}=\sqrt{1}=1unit$

$BC=\sqrt{{(1-0)}^2+{(1-0)}^2}=\sqrt{1^2+1^2}=\sqrt{2}units$ 

$CA=\sqrt{{(0-0)}^2+{(0-1)}^2}=\sqrt{1^2}=1units$

$AB+BC+CA=1+\sqrt{2}+1=2+\sqrt{2}$