A rectangular box has vertices at (0,0,0), (8,0,0), (0,6,0), and (0,0,24). What is the length of the space diagonal of this box?
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Correct answer
A. 26
Principle or equation
The space diagonal of a rectangular box with side lengths a, b, c is given by √(a^2 + b^2 + c^2).
Why this answer is correct
The box has side lengths 8, 6, and 24 (the distances along the x, y, z axes from the origin to the given vertices). The space diagonal is √(8^2 + 6^2 + 24^2) = √(64 + 36 + 576) = √676 = 26.
Example
For a box with sides 3, 4, 12, the space diagonal is √(9+16+144) = √169 = 13.
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