Question

The sides of a rectangle are in the ratio 3 : 7 and its area is 1029 m². Find the dimensions of the rectangle, and then find its perimeter.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{rectangle}=7\mathrm{x}\mathrm{m} \\ \mathrm{then}\mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{rectangle}=3\mathrm{x}\mathrm{m} \\ \mathrm{Area}\mathrm{of}\mathrm{rectangle}=1029{\mathrm{m}}^2 \\ \Rightarrow \mathrm{length}\times \mathrm{breadth}=1029 \\ \Rightarrow 7\mathrm{x}\times 3\mathrm{x}=1029 \\ \Rightarrow 21{\mathrm{x}}^2=1029 \\ \Rightarrow {\mathrm{x}}^2=\frac{1029}{21} \\ \Rightarrow {\mathrm{x}}^2=49 \\ \Rightarrow \mathrm{x}=7 \\ \mathrm{So},\mathrm{length}=7\mathrm{x}=7\times 7=49\mathrm{m} \\ \mathrm{breadth}=3\mathrm{x}=3\times 7=21\mathrm{m} \\ \mathrm{Perimeter}=2\left[\mathrm{length}+\mathrm{breadth}\right]=2\left[49+21\right]=2\times 70=140\mathrm{m} \end{gathered}$$