Question

if the ratio of the areas of 2 similar polygons is 32:50, what is the ration of the corresponding side lengths?

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


`\bf \cfrac{small}{large}\qquad \cfrac{s}{s}=\cfrac{√(s^2)}{√(s^2)}\implies \cfrac{s}{s}=\cfrac{√(32)}{√(50)}\implies \cfrac{s}{s}=\cfrac{√(16\cdot 2)}{√(25\cdot 2)} \\\\\\ \cfrac{s}{s}=\cfrac{√(4^2\cdot 2)}{√(5^2\cdot 2)}\implies \cfrac{s}{s}=\cfrac{4√(2)}{5√(2)}\implies \cfrac{s}{s}=\cfrac{4}{5}`