Question

The perimeter of a square and a rectangle are equal. The length of the rectangle is three times its breadth and its semi- perimeter is 160 metres. Find the side of the square and length breadth of the rectangle.

Answer 1

Dear student

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{square}=\mathrm{x}\mathrm{m} \\ \mathrm{So},\mathrm{perimeter}\mathrm{of}\mathrm{square}=\left(4\mathrm{x}\right)\mathrm{m} \\ \mathrm{Let}\mathrm{breadth}\mathrm{of}\mathrm{rectangle}=\mathrm{b}\mathrm{m}, \\ \mathrm{So},\mathrm{length}\boxed{\mathrm{l}=\left(3\mathrm{b}\right)\mathrm{m}} \\ \mathrm{Perimeter}\mathrm{of}\mathrm{rectangle}=2\left(\mathrm{l}+\mathrm{b}\right) \\ =2\left(3\mathrm{b}+\mathrm{b}\right) \\ =2\times 4\mathrm{b} \\ =\left(8\mathrm{b}\right)\mathrm{m}. \\ \mathrm{A}.\mathrm{T}.\mathrm{Q} \\ \mathrm{Perimeter}\mathrm{of}\mathrm{square}=\mathrm{Perimeter}\mathrm{of}\mathrm{rectangle} \\ 4\mathrm{x}=8\mathrm{b} \\ \boxed{\mathrm{x}=2\mathrm{b}} \\ \mathrm{Given}:\mathrm{semi}\mathrm{perimeter}\mathrm{of}\mathrm{rectangle}=160\mathrm{m} \\ \mathrm{l}+\mathrm{b}=160 \\ \Rightarrow 3\mathrm{b}+\mathrm{b}=160 \\ \Rightarrow 4\mathrm{b}=160 \\ \Rightarrow \boxed{\mathrm{b}=40\mathrm{m}} \\ \mathrm{So},\mathbf{}\mathbf{breadth}\mathbf{}\mathbf{of}\mathbf{}\mathbf{rectangle}\mathbf{=}\mathbf{40}\mathbf{}\mathbf{m} \\ \mathbf{So}\mathbf{,}\mathbf{}\mathbf{length}\mathbf{}\mathbf{of}\mathbf{}\mathbf{rectangle}\mathbf{=}\mathbf{3}\mathbf{\times }\mathbf{b}\mathbf{=}\mathbf{3}\mathbf{\times }\mathbf{40}\mathbf{=}\mathbf{120}\mathbf{}\mathbf{m} \\ \mathrm{and}\mathbf{side}\mathbf{}\mathbf{of}\mathbf{}\mathbf{square}\mathbf{=}\mathbf{2}\mathbf{b}\mathbf{=}\mathbf{2}\mathbf{\times }\mathbf{40}\mathbf{=}\mathbf{80}\mathbf{}\mathbf{m} \end{gathered}$$
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