A box has a base of 12 inches by 12 inches and a height of 30 inches. What is the length of the interior diagonal of the box? Round to the nearest hundredth

First, find the hypotenuse of the right triangle formed by the base:

12^2 + 12^2 = c^2

c = sqrt (288) in

This will now be the length of the base of the new right triangle.

The new right triangle, with the hypotenuse as the interior diagonal, will have sides of length:

Sqrt (288) in & 30 in

Plug these in to the Pythagorean theorem:

Sqrt (288) ^2 + 30^2 = c^2

288 + 900 = c^2

c = 34.47 in

The length of the interior diagonal of the box is 34.47 in.