A straw is placed inside a rectangular box that is 5 inches by 1 inches by 2 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

We are tasked with finding the length of a straw placed diagonally inside a rectangular box with dimensions 5 inches, 1 inch, and 2 inches. The straw stretches from the bottom-left corner of the box to the top-right back corner.

This is a 3D distance problem. To find the length of the straw, we need to compute the diagonal of the rectangular box using the 3-dimensional distance formula:

\[
d = \sqrt{l^2 + w^2 + h^2}
\]
where:
- \(l = 5\) inches (length),
- \(w = 1\) inch (width),
- \(h = 2\) inches (height).

Substitute these values into the formula:

\[
d = \sqrt{5^2 + 1^2 + 2^2}
\]
\[
d = \sqrt{25 + 1 + 4}
\]
\[
d = \sqrt{30}
\]

Thus, the length of the straw is \( \sqrt{30} \) inches. This is the simplest radical form of the answer.

### Final answer:
\[
\boxed{\sqrt{30}} \text{ inches.}
\]

Would you like to go into further details on any part of the solution?

### Related Questions:
1. How do you calculate the diagonal of a rectangle in 2D?
2. Can you explain how to apply the Pythagorean theorem in 3D geometry?
3. What are the steps to simplify square roots?
4. How do you handle problems involving vectors in 3D space?
5. What are some real-life applications of finding diagonals in geometric shapes?

### Tip:
When dealing with 3D problems, visualize each dimension clearly and consider breaking the problem into smaller parts using the Pythagorean theorem.

A straw is placed inside a rectangular box that is 5 inches by 1 inch by 2 inches. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

Learn how to find the diagonal of a rectangular box with dimensions 5 inches by 1 inch by 2 inches. This geometry problem involves the 3D distance formula and Pythagorean theorem. Suitable for students in Grades 9-10, the solution is provided in simplest radical form: √30 inches.

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