[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{smaller}{larger}\qquad \cfrac{3}{4}=\cfrac{\sqrt{13}}{\sqrt{a}}\implies \cfrac{3}{4}=\sqrt{\cfrac{13}{a}}\implies \left( \cfrac{3}{4} \right)^2=\cfrac{13}{a}
\\\\\\
\cfrac{3^2}{4^2}=\cfrac{13}{a}\implies \cfrac{9}{16}=\cfrac{13}{a}\implies a=\cfrac{16\cdot 3}{9}[/tex]
