Broken rectangle border and custom borders

Question

I'm looking for a way to define a style (I do not want to manually draw the edges by hand for each node) that provides a node containing three "normal" edges, and one zigzag edge. Here is an example :

I tried to use decorate, but I didn't obtain good results... By the way, any "general" solution to deal with custom boarders are welcome.

Here is a MWE :

\documentclass{article}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}[
  broken/.style = {
    draw,
    rectangle
  }
  ]
  \node[broken] {Hello};
\end{tikzpicture}

\end{document}

Thank you.

=== EDIT === I found a solution, but I cannot fill the shape, properly, so the question is still open.

Answer 1

Here a solution based on your code, filling and drawing of nodes must be done within brokenrect style.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}

\begin{document}

\tikzset{ brokenrect/.style={
    append after command={
      \pgfextra{
      \path[draw,#1]
       decorate[decoration={zigzag,segment length=0.4em, amplitude=.3mm}]
       {(\tikzlastnode.north east)--(\tikzlastnode.south east)}      
        -- (\tikzlastnode.south west)|-cycle;
        }}}}

\begin{tikzpicture}
  \node [brokenrect={fill=orange,draw=blue},inner sep=10pt] {Coucou};
\end{tikzpicture}

\end{document}

Answer 2

I found this solution, I don't know if it's the more straight forward, but it works pretty well, and is quite clear I think. The problem of it is that the filling is very ugly, so any better solution would be nice.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}

\begin{document}

\begin{tikzpicture}[
  brokenrect/.style={
    append after command={
      \pgfextra{
        \draw[] (\tikzlastnode.south west) |- (\tikzlastnode.north east);
        \draw[] (\tikzlastnode.south west) -- (\tikzlastnode.south east);
        \draw[decorate,decoration={zigzag,segment length=0.4em,amplitude=0.1em}] (\tikzlastnode.north east) -- (\tikzlastnode.south east);
      }
    }
  }
  ]
  \node [brokenrect] {Coucou};
\end{tikzpicture}

\end{document}

Here is the result in picture :

and the ugly filling :