A rectangle of length ‘x’ and breadth ‘y’ is inscribed in a semi-circle of fixed radius ‘r’ as shown in the figure given below.

Based on the above information answer the following question:

Perimeter of rectangle when its area is maximum is:

\(3\sqrt{2}r\)

Perimeter of rectangle = 2(L + B)

So max. perimeter = $2(r\sqrt{2}+\frac{r}{\sqrt{2}})⇒2r(\frac{\sqrt{2}×\sqrt{2}+1}{\sqrt{2}})$

$=2r[\frac{2+1}{\sqrt{2}}]⇒2r[\frac{3}{\sqrt{2}}]$

$=2r(\frac{3}{\sqrt{2}})×\frac{\sqrt{2}}{\sqrt{2}}=2r×\frac{3\sqrt{2}}{2}=3\sqrt{2}r$

So, option D is correct.