Answer:
36.50 in
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.