Question

Find the length of the side of the square whose area is to the area of rectangle with side 25 metre and 20 metre respectively, given that square root 5 =2.236

Answer 1

$$\begin{gathered} \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{rectangle}=25\mathrm{m} \\ \mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{rectangle}=20\mathrm{m} \\ \mathrm{Area}\mathrm{of}\mathrm{rectangle}=\mathrm{length}\times \mathrm{breadth} \\ \Rightarrow \mathrm{area}\mathrm{of}\mathrm{rectangle}=25\times 20=500{\mathrm{m}}^2 \\ \mathrm{Now},\mathrm{area}\mathrm{of}\mathrm{square}=\mathrm{area}\mathrm{of}\mathrm{rectangle} \\ \mathrm{so},\mathrm{area}\mathrm{of}\mathrm{square}=500{\mathrm{m}}^2 \\ \Rightarrow {\mathrm{s}}^2=500\mathbf{}\left[\mathbf{where}\mathbf{}\mathbf{s}\mathbf{}\mathbf{=}\mathbf{}\mathbf{length}\mathbf{}\mathbf{of}\mathbf{}\mathbf{each}\mathbf{}\mathbf{side}\mathbf{}\mathbf{of}\mathbf{}\mathbf{square}\right] \\ \Rightarrow \mathrm{s}=\sqrt{500} \\ \Rightarrow \mathrm{s}=\sqrt{2\times 2\times 5\times 5\times 5} \\ \Rightarrow \mathrm{s}=10\sqrt{5} \\ \Rightarrow \mathrm{s}=10\times 2.236=22.36\mathrm{m} \end{gathered}$$