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. Enter your answer in the box.

36.50 in

Step-by-step explanation:

The length of the diagonal of the square base is found using the Pythagorean Theorem: d^2 = (12 in) ^2 + (12 in) ^2, or d = √2 * (12 in), or d = 12√2 in.

We use the Pythagorean Theorem again to find the length of the interior diagonal of the box:

[12√2 in]² + [ (12 in) ² + (30 in) ² = (interior diagonal) ²

This works out to (interior diagonal) ² = 288 + 144 + 900 inches², or

(interior diagonal) ² = 1332 in²

Then the interior diagonal is √1332 in, or approximately 36.50 in.