Question

The widths of two similar rectangles are 16 cm and 14 cm. What is the ratio of the areas?

Answer 1

`\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} \\\\ -----------------------------\\\\`


`\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{√(s^2)}{√(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}`