\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usetikzlibrary{shapes, calc, shapes,snakes} 
\usepackage{amsmath,amssymb}

\begin{document}
\begin{preview}
\begin{tikzpicture}[dot/.style={    thick,
    %draw=gray,
    %cross out,
    fill,
    shape=circle,
    inner sep=3pt,
    minimum width=4pt,
    minimum height=4pt}]
    % Draw the triangle
    \draw[fill=green!10]  (0,    0) coordinate (a) 
        -- (5cm,0) coordinate (b) 
        -- (3.6cm,  4.8cm) coordinate (c) 
        -- (0,    0)  -- cycle;

    \draw[fill=blue!10]  (a) 
        -- (b) 
        -- (6.4cm,  4.8cm) coordinate (d) 
        -- (0,    0)  -- cycle;

    \draw[fill=red!10]  (a) 
        -- (b) 
        -- (4.1cm,3.07cm) coordinate (e) 
        -- (0,    0)  -- cycle;

    %\node (a) [dot] at (0,0) {};
    %\node (b) [dot] at (5cm,0) {};
    %\node (c) [dot] at (3.6cm,4.8cm) {};

    \draw[thick] (a) -- (b) node [black,midway,yshift=-0.2cm,sloped] {5cm};
    \draw[thick] (b) -- (c) node [black,midway,yshift=+0.2cm,sloped] {5cm};
    \draw[thick] (a) -- (c) node [black,midway,yshift=+0.2cm,sloped] {6cm};

    \draw[thick] (a) -- (d) node [black,midway,yshift=+0.2cm,sloped] {8cm};
    \draw[thick] (b) -- (d) node [black,midway,yshift=-0.2cm,sloped] {5cm};

%   \draw[dashed,thick,lime] (a) circle(8cm);
%    \draw[dashed,thick,red] (a) circle(6cm);
%    \draw[dashed,thick,lime] (b) circle(5cm);
%    \draw[dashed,thick,red] (b) circle(6cm);
%    \draw[dashed,thick,lime] (c) circle(5cm);
%    \draw[dashed,thick,red] (c) circle(6cm);
\end{tikzpicture}
\end{preview}
\end{document}