The longest line segment that can be drawn in a right rectangular prism is the space diagonal, which is a line segment connecting two opposite vertices of the prism.
To find the length of the space diagonal, we can use the Pythagorean theorem in three dimensions:
d^2 = l^2 + w^2 + h^2
where d is the length of the space diagonal, l is the length of the prism, w is the width of the prism, and h is the height of the prism.
Substituting the given values, we get:
d^2 = 14^2 + 13^2 + 8^2
d^2 = 196 + 169 + 64
d^2 = 429
d = sqrt(429)
d ≈ 20.7 cm
Therefore, the longest line segment that can be drawn in the right rectangular prism is approximately 20.7 cm long.