Question

A rectangle has an area of 20 ft.² in a similar rectangle has an area of 180 ft.² what is the ratio of areas of the similar

Answer 1

$\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{cccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\ -----------------------------$

$\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s^2}{s^2}=\cfrac{20}{180}\implies \left( \cfrac{s}{s} \right)^2=\cfrac{20}{180}\implies \cfrac{s}{s}=\sqrt{\cfrac{20}{180}} \\\\\\ \cfrac{s}{s}=\cfrac{\sqrt{20}}{\sqrt{180}}\implies \cfrac{s}{s}=\cfrac{2\sqrt{5}}{6\sqrt{5}}\implies \cfrac{s}{s}=\cfrac{2}{6}\implies \cfrac{s}{s}=\cfrac{1}{3}$