Question

The length and breadth of a rectangular park are in the ratio 5 : 3 and its perimeter is 128 m. Find the area of the park.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{park}\mathrm{be}5x\mathrm{m}\mathrm{and}\mathrm{its}\mathrm{breadth}\mathrm{be}3x\mathit{}\mathrm{m}. \\ \mathrm{As},\mathrm{perimeter}\mathrm{of}\mathrm{the}\mathrm{park}=2\times \left(\mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{park}+\mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{park}\right) \\ =2\times \left(5x+3x\right) \\ =2\times 8x \\ =16x\mathrm{m} \\ \mathrm{But}\mathrm{the}\mathrm{perimeter}\mathrm{of}\mathrm{the}\mathrm{park}=128\mathrm{m} \\ \Rightarrow 16x=128 \\ \Rightarrow x=\frac{128}{16} \\ \Rightarrow x=8 \\ \therefore \mathrm{The}\mathrm{length}\mathrm{of}\mathrm{park}=5x=5\times 8=40\mathrm{m}\mathrm{and} \\ \mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{park}=3x=3\times 8=24\mathrm{m} \\ \mathrm{Now},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{park}=\mathrm{Length}\times \mathrm{Breadth} \\ =40\times 24 \\ =960{\mathrm{m}}^2 \end{gathered}$$

So, the area of the park is 960 m².