Question

The area of a rectangular field whose length is twice its breadth is 684.5m square. Find the perimeter of the field

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{width}=\mathrm{x}\mathrm{m} \\ \mathrm{then}\mathrm{the}\mathrm{length}=2\mathrm{x}\mathrm{m} \\ \mathrm{Area}=684.5{\mathrm{m}}^2 \\ \Rightarrow \mathrm{length}\times \mathrm{breadth}=684.5 \\ \Rightarrow 2{\mathrm{x}}^2=684.5 \\ \Rightarrow {\mathrm{x}}^2=342.25 \\ \Rightarrow \mathrm{x}=\sqrt{342.25}=18.5 \\ \mathrm{Now},\mathrm{breadth}=18.5\mathrm{m} \\ \mathrm{length}=2\times 18.5=37\mathrm{m} \\ \mathrm{Perimeter}=2\left(\mathrm{length}+\mathrm{width}\right) \\ =2\left(37+18.5\right) \\ =2\times 55.5 \\ =111\mathrm{m} \end{gathered}$$