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What is the longest line segment that can be drawn in a right rectangular prism that is 14 cm​ long, 13 cm​ wide, and 8 cm​ tall?

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User Roman C
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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.
User Ahsan Naseem
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