A rectangular box has vertices at (0,0,0), (6,0,0), (0,8,0), and (0,0,24). What is the length of the space diagonal of this box?
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Correct answer
B. 26
Principle or equation
The space diagonal of a rectangular box with side lengths a, b, c is sqrt(a^2 + b^2 + c^2).
Why this answer is correct
The side lengths are 6, 8, and 24. The space diagonal is sqrt(6^2 + 8^2 + 24^2) = sqrt(36 + 64 + 576) = sqrt(676) = 26.
Example
For a box with sides 3,4,12, the diagonal is sqrt(9+16+144)=sqrt(169)=13.
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