CAT 2020 Exam Shift 1 Solved Paper

Let the length and the breadth of the rectangle be 1 and b respectively.
As the circle touches the two opposite sides, its diameter will be same as the breadth of the rectangle. Given, $\mathit{l}\mathit{b}=135$ and $\mathit{l}\mathit{b}=\mathit{\pi }{\left(\frac{\mathit{b}}{2}\right)}^2=\frac{2}{3}\times \mathit{\pi }{\left(\frac{\mathit{b}}{2}\right)}^2$
$\Rightarrow \frac{5}{3}\mathit{\pi }\left(\frac{{\mathit{b}}^2}{4}\right)=135\Rightarrow \mathit{b}=\frac{18}{\sqrt{\mathit{\pi }}}$
From this $\mathit{l}=\frac{15\sqrt{\mathit{\pi }}}{2}$
$\therefore$ Required perimeter: