Question

The length of a rectangle is 5/4of its breadth. If the perimeter is 81m. Find its area.

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{rectangle}=\mathrm{b}\mathrm{m} \\ \mathrm{So},\mathrm{length}\mathrm{of}\mathrm{rectangle},\mathrm{l}=\frac{5}{4}\times \mathrm{b}=\frac{5\mathrm{b}}{4}...\left(1\right) \\ \mathrm{Given}:\mathrm{perimeter}\mathrm{of}\mathrm{rectangle},\mathrm{P}=81\mathrm{m} \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{Perimeter}\mathrm{of}\mathrm{rectangle}=2\left(\mathrm{l}+\mathrm{b}\right) \\ 81=2\left(\frac{5\mathrm{b}}{4}+\mathrm{b}\right) \\ \Rightarrow 40.5=\frac{9\mathrm{b}}{4} \\ \Rightarrow 162=9\mathrm{b} \\ \Rightarrow \mathrm{b}=18\mathrm{m} \\ \mathrm{So},\mathrm{l}=\frac{5}{4}\times 18\left[\mathrm{using}\left(1\right)\right] \\ =22.5\mathrm{m} \\ \mathrm{Area}\mathrm{of}\mathrm{rectangle}=\mathrm{l}\times \mathrm{b}=22.5\times 18=405{\mathrm{m}}^2 \end{gathered}$$
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