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:
Answer & explanation
Correct answer: option 4
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.