Question

1.Find the ratio of the areas of two squares whose sides are in ratio 2:3.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{first}\mathrm{square},{\mathrm{s}}_1=2\mathrm{x}\mathrm{units} \\ \mathrm{then}\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{second}\mathrm{square},{\mathrm{s}}_2=3\mathrm{x}\mathrm{units} \\ \mathrm{Area}\mathrm{of}\mathrm{first}\mathrm{square},{\mathrm{A}}_1={{\mathrm{s}}_1}^2={\left(2\mathrm{x}\right)}^2=4{\mathrm{x}}^2\mathrm{sq}\mathrm{units} \\ \mathrm{Area}\mathrm{of}\mathrm{second}\mathrm{square},{\mathrm{A}}_2={{\mathrm{s}}_2}^2={\left(3\mathrm{x}\right)}^2=9{\mathrm{x}}^2\mathrm{sq}\mathrm{units} \\ \mathrm{Now},\frac{{\mathrm{A}}_1}{{\mathrm{A}}_2}=\frac{4{\mathrm{x}}^2}{9{\mathrm{x}}^2}=\frac{4}{9}=4:9 \end{gathered}$$