Question

the length of a rectangle is 15 cm greater than its breadth. its perimeter is 150 cm. find the dimensions of the rectangle.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{rectangle}=\mathrm{x}\mathrm{cm} \\ \mathrm{Now},\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{rectangle}=\left(\mathrm{x}+15\right)\mathrm{cm} \\ \mathrm{Perimeter}\mathrm{of}\mathrm{the}\mathrm{rectangle}=150\mathrm{cm} \\ \Rightarrow 2\left[\mathrm{length}+\mathrm{breadth}\right]=150 \\ \Rightarrow \left(\mathrm{x}+15+\mathrm{x}\right)=75 \\ \Rightarrow 2\mathrm{x}+15=75 \\ \Rightarrow 2\mathrm{x}=60 \\ \Rightarrow \mathrm{x}=\frac{60}{2}=30 \\ \mathrm{So},\mathrm{length}\mathrm{of}\mathrm{rectangle}=30+15=45\mathrm{cm} \\ \mathrm{breadth}\mathrm{of}\mathrm{rectangle}=30\mathrm{cm} \end{gathered}$$