What is the measurement of the longest line segment in a right rectangular prism that is 26 inches long, 2 inches wide, and 2 inches tall?

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,)

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,

. 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.

answer: do we write it

step-by-step explanation: