Question

Each side of a square field measures 21 m. Adjacent to this field, there is a rectangular field having its sides in the ratio 4 : 3. If the perimeters of both the fields are equal, find the dimensions of the rectangular field.

Answer 1

Side of the square field = 21m
Perimeter of the square field = (4$\times$21) m
= 84 m

Let the length and the breadth of the rectangular field be 4x and 3x, respectively.
Perimeter of the rectangular field = 2(4x + 3x) = 14x

Perimeter of the rectangular field = Perimeter of the square field

$$\begin{gathered} \therefore 14x=84 \\ \Rightarrow x=\frac{84}{14}=6 \end{gathered}$$
$$\begin{gathered} \therefore \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{field}=(4\times 6)\mathrm{m}=24\mathrm{m} \\ \mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{field}=(3\times 6)\mathrm{m}=18\mathrm{m} \end{gathered}$$