Answer:
inches.
Step-by-step explanation:
The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment 
.
In this diagram (not to scale,) 
(length of prism,) 
(width of prism,) 
(height of prism.)
Pythagorean Theorem can help find the length of , one of the longest line segments in this prism. However, note that this theorem is intended for right triangles in 2D, not the diagonal in a 3D prism. The workaround is to simply apply this theorem on two different right triangles.
Start by finding the length of line segment 
. That's the black dotted line in the diagram. In right triangle 
(second diagram,)
- Segment is the hypotenuse.
- One of the legs of is
. The length of is 
, same as the length of this prism. - Segment
is the other leg of this triangle. The length of is 
, same as the width of this prism.
Apply the Pythagorean Theorem to right triangle to find the length of , the hypotenuse of this triangle:
.
Consider right triangle 
(third diagram.) In this triangle,
- Segment is the hypotenuse, while
- and
are the two legs.
. The length of segment is the same as the height of the rectangular prism, (inches.) Apply the Pythagorean Theorem to right triangle to find the length of the hypotenuse :
.
Hence, the length of the longest line segment in this prism is inches.
