Answer:
Longest line segment: 12.89 cm
Step-by-step explanation:
Right Rectangular Prism
A right rectangular-based prism has a height measured from the center of the base up to the top of the prism. The longest line segment can be:
1. Any of the provided dimensions of the base or
2. A drawn line from the top ending in any of the corners of the base. It's the hypotenuse of a triangle whose legs are: the height of the prism and half the diagonal of the rectangle of the base.
The construction of the triangles can be seen in the figure attached. The line segment we are required to compute is the solid red line.
Let's first compute the diagonal of the rectangle of sides 12 cm and 11 cm.
[tex]d=\sqrt{12^2+11^2}=16.28\ cm[/tex]
Half of the diagonal is
[tex]d/2=8.14\ cm[/tex]
Finally, we find the hypotenuse of the triangle formed by d/2, h, and the required distance, let's call it p
[tex]p=\sqrt{8.14^2+10^2}=12.89\ cm[/tex]
This length is greater than the 12 cm side of the rectangle, so it confirms our initial guess, the longest line segment is 12.89 cm long.
Note if the height would have been, for example, 5 cm, the longest line would have been 12 cm, and not the one found by the procedure
