Question

If the scale factor between two circles is 2x/5y, what is the ratio of their 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} \\\\ -----------------------------\\\\ \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{s}{s}=\cfrac{2x}{5y}\qquad \textit{then the areas ratio is }\cfrac{s^2}{s^2}\implies \cfrac{(2x)^2}{(5y)^2}\implies \cfrac{4x^2}{25y^2}`