Move line by size of arrow tip

Question

I'm trying to draw a simple rectangle together with the dimensions. Here is my first try:

\documentclass{article}

\usepackage{tikz}

\begin{document}
    \pgfmathsetmacro{\a}{2.0}
    \pgfmathsetmacro{\b}{4.0}
    \begin{tikzpicture}
        \draw (0, 0) rectangle (\a, \b);
        \draw[|<->|] (0, 0) -- ++ (\a, 0); 
        \node[below] at (0.5*\a, 0) {a};
    \end{tikzpicture}
\end{document}

This of course results in the line drawn on top of the rectangle, but I would like it to be a bit below. Sure, I could do something like

\draw[|<->|] (0, -5mm) -- ++ (\a, 0); 

but this is neither very nice nor does it scale correctly. Any suggestions?

Edit: Heres is an example of what I mean by not scaling correctly:

\documentclass{article}

\pagestyle{empty}
\usepackage{tikz}

\begin{document}
    \pgfmathsetmacro{\a}{2.0}
    \pgfmathsetmacro{\b}{4.0}
    \begin{tikzpicture}[scale=1]
        \draw (0, 0) rectangle (\a, \b);
        \draw[|<->|] ([yshift=-1mm]0, 0) -- ++ (\a, 0); 
        \node[below] at (0.5*\a, 0) {a};
    \end{tikzpicture}
    \begin{tikzpicture}[scale=5]
        \draw (0, 0) rectangle (\a, \b);
        \draw[|<->|] ([yshift=-1mm]0, 0) -- ++ (\a, 0); 
        \node[below] at (0.5*\a, 0) {a};
    \end{tikzpicture}
\end{document}

Answer 1

Here is a layman's workaround where we define a node at (0,0) and then draw the arrow from its south.

\documentclass{article}
\usepackage{tikz}

\begin{document}
    \pgfmathsetmacro{\a}{2.0}
    \pgfmathsetmacro{\b}{4.0}
    \begin{tikzpicture}[scale=1]
        \draw (0, 0) node[below] (A){} rectangle (\a, \b);
        \draw[|<->|] (A.south) -- ++ (\a, 0);
        \node[below] at (0.5*\a, 0) {a};
    \end{tikzpicture}
    \begin{tikzpicture}[scale=3]
        \draw (0, 0) node[below] (A){} rectangle (\a, \b);
        \draw[|<->|] (A.south) -- ++ (\a, 0);
        \node[below] at (0.5*\a, 0) {a};
    \end{tikzpicture}
\end{document}

You can vary the distance by changing the inner sep

\draw (0, 0) node[inner sep=1mm,below] (A){} rectangle (\a, \b);