A rectangular box has vertices at (0,0,0), (4,0,0), (0,3,0), and (0,0,12). What is the length of the space diagonal of this box?
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Correct answer
C. 13
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 4, 3, and 12. The diagonal is sqrt(4^2 + 3^2 + 12^2) = sqrt(16 + 9 + 144) = sqrt(169) = 13.
Example
For a cube of side 2, diagonal = sqrt(4+4+4) = sqrt(12) = 2√3.
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