Answer : Option D

Explanation :

$MF#%\boxed{\text{For a rectangle, }d^2 = l^2 + b^2 \\\\
\text{where l = length , b = breadth and d = diagonal of the of the rectangle}}$MF#%

$MF#%\begin{align}
&d = \sqrt{41}\text{ cm}\\\\
&d^2 = l^2 + b^2\\\\
&\Rightarrow l^2 + b^2 = \left(\sqrt{41}\right)^2 = 41\text{........(Equation 1)}\\\\\\\\\\\\
&\text{Area = lb = 20 cm}^2\text{............(Equation 2)}\\\\\\\\\\\\
&\text{Solving (Equation 1) and (Equation 2)}\\
&\end{align} $MF#%

$MF#%\boxed{(a + b)^2 = a^2 + 2ab + b^2}$MF#%

$MF#%\begin{align}
&\text{using the above formula, we have}\\\\
&(l + b)^2 = l^2 + 2lb + b^2 = (l^2 + b^2) + 2lb = 41 + (2 \times 20) = 81\\\\
&\Rightarrow (l + b) = \sqrt{81} = 9 \text{ cm}\\\\
&\text{perimeter = }2(l + b) = 2 \times 9 = 18\text{ cm}
\end{align} $MF#%