Question

the perimeter of a rectangular field is 3/5 km. if the length of the field is twice its width find the area of the rectangle in m sq

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{width}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{field}=x\mathrm{metre} \\ \mathrm{then}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{field}=2x\mathrm{metre} \\ \mathrm{Now},\mathrm{perimeter}\mathrm{of}\mathrm{the}\mathrm{field}=\frac{3}{5}\mathrm{km}=\left[\frac{3}{5}\times 1000\right]\mathrm{m}=600\mathrm{m} \\ \Rightarrow 2\left(\mathrm{length}+\mathrm{breadth}\right)=600 \\ \Rightarrow \mathrm{length}+\mathrm{breadth}=300 \\ \Rightarrow 2x+x=300 \\ \Rightarrow 3x=300 \\ \Rightarrow \boxed{x=100} \\ \mathrm{Now},\mathrm{width}\mathrm{of}\mathrm{the}\mathrm{field}=100\mathrm{m} \\ \mathrm{length}\mathrm{of}\mathrm{the}\mathrm{field}=2\times 100=200\mathrm{m} \\ \mathrm{Now},\mathrm{area}=\mathrm{length}\times \mathrm{breadth}=200\times 100=20000{\mathrm{m}}^2 \end{gathered}$$