[tex]\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{cccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\
-----------------------------\\\\
thus
\\\\\\
\cfrac{75}{12}=\cfrac{s^2}{s^2}\implies \cfrac{75}{12}=\left( \cfrac{s}{s} \right)^2\implies \sqrt{\cfrac{75}{12}}=\cfrac{s}{s}
\\\\\\
[/tex]
[tex]\bf \cfrac{\sqrt{75}}{\sqrt{12}}=\cfrac{s}{s}\impliedby
\begin{array}{llll}
\textit{ratio of the sides}\\
\textit{and thus of the perimeter}
\end{array}[/tex]
