Question

The length and the 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

Let the length of the rectangular park be 5x.
∴ Breadth of the rectangular park = 3x
Perimeter of the rectangular field = 2(Length + Breadth)
=2(5x + 3x)
= 16x

It is given that the perimeter of rectangular park is 128 m.
$$\begin{gathered} \Rightarrow 16\mathrm{x}=128 \\ \Rightarrow \mathrm{x}=\frac{128}{16} \\ \Rightarrow \mathrm{x}=8 \\ \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{park}=(5\times 8)\mathrm{m} \\ =40\mathrm{m} \\ \mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{park}=(3\times 8)\mathrm{m} \\ =24\mathrm{m} \end{gathered}$$

Area of the park = (Length $\times$ Breadth) sq units

$$\begin{gathered} =(40\times 24){\mathrm{m}}^2 \\ =960{\mathrm{m}}^2 \end{gathered}$$