Question

The area of a square field is 1/2 hectares. Find the length of its diagonals.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{side}\mathrm{of}\mathrm{square}=\mathrm{s} \\ \mathrm{Now},\mathrm{area}\mathrm{of}\mathrm{square}=0.5\mathrm{ha}=5000{\mathrm{m}}^2\left[\mathrm{as}1\mathrm{ha}=10000{\mathrm{m}}^2\right] \\ \mathrm{Now},{\mathrm{s}}^2=5000 \\ \Rightarrow \mathrm{s}=\sqrt{5000}=50\sqrt{2}\mathrm{m} \\ \mathrm{Now},\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{diagonal}=\sqrt{2}\mathrm{s}=50\times \sqrt{2}\times \sqrt{2}=100\mathrm{m} \end{gathered}$$