Answer : Option A

Explanation :

The longest road which can fit into the box will have one end at A and
other end at G (or any other similar diagonal)
Hence the length of the longest rod = AG
Initially let's find out AC. Consider the right angled triangle ABC

AC² = AB² + BC² = 40² + 80² = 1600 + 6400 = 8000

$MF#%\Rightarrow \text{AC = }\sqrt{8000}\text{ cm}$MF#%

$MF#%\begin{align}&= \left(\sqrt{8000}\right)^2 + 60^2 = 8000 + 3600 = 11600\\\\
&\Rightarrow \text{AG = }\sqrt{11600}\text{ cm}\\\\
&\Rightarrow \text{The length of the longest rod = }\sqrt{11600}\text{ cm}
\end{align} $MF#%