CAT 2023 Slot 3 Solved Paper

Let us assume the length of the rectangle is 'l' and breadth of the rectangle is 'b'.The radius, $\mathrm{l}/2$ and $\mathrm{b}$ in the above diagram form a right-angled triangle.
$\Rightarrow {\left(\frac{\mathit{l}}{2}\right)}^2+{\mathit{b}}^2=2^2$
We know that the area of the rectangle is $\mathrm{l}*\mathrm{b}$, which can be obtained by considering 2 times the geometric mean of ${\left(\frac{\mathit{l}}{2}\right)}^2$ and ${\mathit{b}}^2$.
Therefore, for the maximum area, the equality condition of AM-GM inequality should be satisfied
$\Rightarrow {\left(\frac{\mathit{l}}{2}\right)}^2={\mathit{b}}^2\Rightarrow \mathit{l}=2\mathrm{b}.$
$\Rightarrow 1/\mathrm{b}=2/1.$