To solve this problem, we need to determine the length of the diagonal of a 12-inch square box. The diagonal of a square can be calculated using the Pythagorean theorem:

$\text{Diagonal} = \sqrt{\text{side}^2 + \text{side}^2}$

For a square with side length $12$ inches:

$\text{Diagonal} = \sqrt{12^2 + 12^2} = \sqrt{144 + 144} = \sqrt{288}$

Simplifying further:

$\sqrt{288} \approx 16.97$

To the nearest inch, the diagonal is approximately 17 inches.

Would you like a detailed explanation of the steps or have any questions?

Here are 5 related questions for practice:

1. What is the diagonal of a square with side length 10 inches?
2. How would you find the diagonal of a rectangle with dimensions 8 inches by 15 inches?
3. If a square has a diagonal of 20 inches, what is its side length?
4. How does the Pythagorean theorem apply to finding the diagonal of a square?
5. If a box has a diagonal of 25 inches, what is the smallest square side length that could fit it?

Tip: Always remember to check your units (e.g., inches, cm) when solving geometric problems!