The equation of the base of an equilateral triangle is $x-y-3=0$ and one vertex is $(-1,2)$, then the length of the side is

Perpendicular distance from $(-1,2)$  to the line $x-y+3=0$ is 

$\left|\frac{1(-1)-1\left(2\right)-3}{\sqrt{1^2+{(-1)}^2}}\right|$

$AD=\frac{6}{\sqrt{2}}$

Let $AB=x$

then $BD=\frac{x}{2}$

$\begin{array}{l}{x}^2={\left(\frac{x}{2}\right)}^2+{\left(\frac{6}{\sqrt{2}}\right)}^2\\ x^2=\frac{x^2}{4}+\frac{36}{2}\\ x^2=\frac{x^2+72}{4}\\ 4x^2-x^2=72\\ x^2=24\\ x=\sqrt{24}\end{array}$

de of equilateral triangle$=2\sqrt{6}$.