What is the longest line segment that can be drawn in a right rectangular prism that is 14 cm long, 9 cm wide, and 7 cm tall?

The longest line segment is the main diagonal.

If you want the length of it:

\(\begin{array}{cl} &\text{Length of main diagonal}\\ =& \sqrt{14^2 + 9^2 + 7^2}\\ =& \sqrt{326} \end{array}\)