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.

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step-by-step explanation: