Question

find the cost of constructing a fence around a square field whose area is 90,000sq.m. if fencing costs Rs 35 per metre

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{square}\mathrm{field}=s\mathrm{metres} \\ \mathrm{Area}\mathrm{of}\mathrm{square}\mathrm{field}=90000{\mathrm{m}}^2 \\ \Rightarrow s^2=90000 \\ \Rightarrow s\mathit{}=\sqrt{90000} \\ \Rightarrow s\mathit{}=\sqrt{2\times 2\times 2\times 2\times 3\times 3\times 5\times 5\times 5\times 5} \\ \Rightarrow s=2\times 2\times 3\times 5\times 5 \\ \Rightarrow s=300\mathrm{m} \\ \mathrm{Now}, \\ \mathrm{perimeter}\mathrm{of}\mathrm{the}\mathrm{square}\mathrm{field}=4\mathit{}s=4\times 300=1200\mathrm{m} \\ \mathrm{Cost}\mathrm{of}\mathrm{fencing}1\mathrm{m}\mathrm{of}\mathrm{the}\mathrm{field}=\mathrm{Rs}35 \\ \mathrm{So},\mathrm{cost}\mathrm{of}\mathrm{fencing}1200\mathrm{m}\mathrm{of}\mathrm{the}\mathrm{field}=\mathrm{Rs}\left(1200\times 35\right)=\mathrm{Rs}42000 \end{gathered}$$