Question

A pair of adjacent sides of a rectangle are in the ratio 4:3. If its diagonal is 20 cm. Find the lengths of the sides and hence the perimeter of the rectangle.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{rectangle}=4x\mathrm{cm} \\ \mathrm{then}\mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{rectangle}=3x\mathrm{cm} \\ \mathrm{Now},\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{diagonal}=20\mathrm{cm} \\ \Rightarrow \sqrt{{\left(\mathrm{length}\right)}^2+{\left(\mathrm{breadth}\right)}^2}=20 \\ \Rightarrow \sqrt{{\left(4x\right)}^2+{\left(3x\right)}^2}=20 \\ \Rightarrow \sqrt{16x^2+9x^2}=20 \\ \Rightarrow \sqrt{25x^2}=20 \\ \Rightarrow 5x=20 \\ \Rightarrow x=4 \\ \mathrm{Now},\mathrm{length}=4x=4\times 4=16\mathrm{cm} \\ \mathrm{breadth}=3x=3\times 4=12\mathrm{cm} \\ \mathrm{Now},\mathrm{perimeter}=2\left(\mathrm{length}+\mathrm{breadth}\right)=2\left(16+12\right)=2\times 28=56\mathrm{cm} \end{gathered}$$