Question

two equilateral triangles having their areas in the ratio 36:9, then find the ratio of their corresponding height

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{each}\mathrm{triangle}\mathrm{is}\mathrm{a}\mathrm{and}\mathrm{b}. \\ \mathrm{Equilateral}\mathrm{triangles}\mathrm{are}\mathrm{similar}\mathrm{triangles}. \\ \mathrm{So}, \\ \mathrm{Ratio}\mathrm{of}\mathrm{area}\mathrm{of}\mathrm{triangles}=\mathrm{ratio}\mathrm{of}\mathrm{the}\mathrm{square}\mathrm{of}\mathrm{sides} \\ \mathrm{So}, \\ \mathrm{ratio}\mathrm{of}\mathrm{square}\mathrm{of}\mathrm{sides}=\frac{36}{9}={\left(\frac{6}{3}\right)}^2 \\ \mathrm{ratio}\mathrm{of}\mathrm{sides}=\frac{\mathrm{a}}{\mathrm{b}}=\frac{6}{3} \\ \frac{\mathrm{a}}{\mathrm{b}}=\frac{2}{1} \\ \mathrm{For}\mathrm{equilateral}\mathrm{triangle}\mathrm{height}=\frac{\sqrt{3}\mathrm{side}}{2} \\ \mathrm{Ratio}\mathrm{of}\mathrm{height}=\frac{\left(\frac{\sqrt{3}\mathrm{a}}{2}\right)}{\left(\frac{\sqrt{3}\mathrm{b}}{2}\right)}=\frac{\mathrm{a}}{\mathrm{b}}=\frac{2}{1}=2:1\mathrm{ANS}... \end{gathered}$$