\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A folding stool is modeled geometrically with segments \(\Segment{CB}\) and \(\Segment{AD}\) for the metal frame and segment \(\Segment{CD}\) for the fabric seat. Given \(CG=DG=30\) cm, \(AG=BG=45\) cm, and \(AB=51\) cm, and knowing that the seat \(\Line{CD}\) is parallel to the ground represented by \(\Line{AB}\):
\includegraphics[width=3cm]{\imagepath tabouret.png}
Calculate the length of the seat \(CD\). Justify.
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