How do you calculate the longest diagonal of a cuboid?

To determine the longest diagonal of a cuboid, the best method is to use the Pythagorean theorem. This is because a cuboid has three dimensions: length, width, and height, which can be treated as a right-angled triangle in three-dimensional space.

When you consider the longest diagonal, it stretches from one vertex of the cuboid to the opposite vertex. To find this diagonal, you can first calculate the diagonal of the base face (which is itself a rectangle) using the lengths of the two dimensions of that face. Then, you take this result and apply the Pythagorean theorem again to include the height of the cuboid. This involves using the formula:

[ d = \sqrt{l^2 + w^2 + h^2} ]

where ( d ) is the diagonal, ( l ) is the length, ( w ) is the width, and ( h ) is the height of the cuboid. This formula effectively combines the two-dimensional diagonal with the vertical height to yield the three-dimensional diagonal.

By following this approach, you are ensuring that all dimensions are accounted for in a systematic way, thereby giving you the precise measurement of the longest diagonal across the cuboid