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Reviewed CSCA Mathematics question · Easy

A rectangular prism has vertices at (0,0,0), (4,0,0), (0,6,0), and (0,0,12). What is the length of the space diagonal of this prism?

  1. 10
  2. 14
  3. 22
  4. √52
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Correct answer

B. 14

Principle or equation

The space diagonal of a rectangular prism with side lengths a, b, c is given by √(a² + b² + c²).

Why this answer is correct

The given vertices define a rectangular prism with side lengths 4, 6, and 12. The space diagonal d = √(4² + 6² + 12²) = √(16 + 36 + 144) = √196 = 14.

Example

For a box with dimensions 3, 4, and 12, the space diagonal is √(9 + 16 + 144) = √169 = 13.

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