Question

the length of a rectangle is 5 cm less than twice its breadth . if the length is decreased by 3 cm and the breadth is increased by 2 cm , the perimeter of the resulting rectangle is 72 cm find the area of original rectangle?
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Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{rectangle}=\mathrm{x}\mathrm{cm} \\ \mathrm{and}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{rectangle}=2\mathrm{x}-5\mathrm{cm} \\ \mathrm{We}\mathrm{know}\mathrm{that} \\ \mathrm{perimeter}\mathrm{of}\mathrm{the}\mathrm{rectangle}=2\left(\mathrm{length}+\mathrm{breadth}\right) \\ \mathrm{A}.\mathrm{T}.\mathrm{Q} \\ \mathrm{new}\mathrm{length}=2\mathrm{x}-5-3=2\mathrm{x}-8 \\ \mathrm{and}\mathrm{new}\mathrm{breadth}=\mathrm{x}+2 \\ \mathrm{So}\mathrm{perimetr}=72 \\ \mathrm{ie} \\ 72=2\left(2\mathrm{x}-8+\mathrm{x}+2\right) \\ 72=2\left(3\mathrm{x}-6\right) \\ 36=3\mathrm{x}-6 \\ 42=3\mathrm{x} \\ \mathrm{x}=14\mathrm{cm}=\mathrm{breadth} \\ \mathrm{so}\mathrm{length}=23\mathrm{cm} \\ \mathrm{So}\mathrm{area}\mathrm{of}\mathrm{original}\mathrm{rectangle}=\mathrm{l}\times \mathrm{b}=322{\mathrm{cm}}^2 \end{gathered}$$
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