Question

Describe the relationship between the similarity ratio of two triangles and the ratio of their areas.

Answer 1

`\bf \textit{let's say the sides ratio is }\cfrac{\bigtriangleup_1}{\bigtriangleup_2}\qquad \cfrac{s_1}{s_2} \\\\\\ \textit{then the ratio of their areas is }\cfrac{\bigtriangleup_1}{\bigtriangleup_2}\qquad \cfrac{(s_1)^2}{(s_2)^2}\\\\ -------------------------------\\\\`


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