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Reviewed CSCA Mathematics question · Hard

A rectangular box has dimensions 6, 8, and 24. What is the length of the space diagonal of the box?

  1. 26
  2. 28
  3. 30
  4. 32
Show the answer and explanation

Correct answer

A. 26

Principle or equation

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

Why this answer is correct

Substitute the given dimensions: d = 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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