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Reviewed CSCA Mathematics question · Hard

A rectangular box has dimensions 5, 12, and 13. What is the length of the space diagonal of the box?

  1. sqrt(338)
  2. sqrt(194)
  3. sqrt(250)
  4. sqrt(314)
Show the answer and explanation

Correct answer

A. sqrt(338)

Principle or equation

The space diagonal d of a rectangular box with side lengths a, b, c is d = sqrt(a^2 + b^2 + c^2).

Why this answer is correct

d = sqrt(5^2 + 12^2 + 13^2) = sqrt(25 + 144 + 169) = sqrt(338).

Example

For a box with sides 3, 4, 12, d = sqrt(9 + 16 + 144) = sqrt(169) = 13.

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