Respuesta :
[tex]\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&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} \\\\
-----------------------------\\\\[/tex]
[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \cfrac{rectangle}{rectangle}\qquad \qquad \stackrel{\textit{ratio of sides}}{\cfrac{16}{14}}\qquad \qquad \stackrel{\textit{ratio of areas}}{\cfrac{16^2}{14^2}}\implies \cfrac{256}{196}\implies \cfrac{64}{49}[/tex]
[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \cfrac{rectangle}{rectangle}\qquad \qquad \stackrel{\textit{ratio of sides}}{\cfrac{16}{14}}\qquad \qquad \stackrel{\textit{ratio of areas}}{\cfrac{16^2}{14^2}}\implies \cfrac{256}{196}\implies \cfrac{64}{49}[/tex]
