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Reviewed CSCA Mathematics question · Easy

A rectangular prism has vertices at (0,0,0), (5,0,0), (0,12,0), and (0,0,9). What is the length of the space diagonal of this prism?

  1. √250
  2. √170
  3. √194
  4. √225
Show the answer and explanation

Correct answer

A. √250

Principle or equation

The space diagonal of a rectangular prism with side lengths a, b, c is √(a^2 + b^2 + c^2).

Why this answer is correct

The side lengths are 5, 12, and 9. The space diagonal is √(5^2 + 12^2 + 9^2) = √(25 + 144 + 81) = √250.

Example

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

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