A straw is placed inside a rectangular box that is 5 inches by 1 inch by 2 inches. The straw fits exactly into the box diagonally from the bottom left corner to the top right back corner. We need to find the length of the straw.

1. Problem Description

A straw is placed inside a rectangular box that is 5 inches by 1 inch by 2 inches. The straw fits exactly into the box diagonally from the bottom left corner to the top right back corner. We need to find the length of the straw.

2. Solution Steps

We can use the 3D Pythagorean theorem to find the length of the straw. Let the length, width, and height of the box be $l$, $w$, and $h$ respectively. The length of the straw, $d$, is given by:

$d = \sqrt{l^2 + w^2 + h^2}$

Given that the length $l = 5$ inches, the width $w = 1$ inch, and the height $h = 2$ inches, we can substitute these values into the formula:

$d = \sqrt{5^2 + 1^2 + 2^2}$

$d = \sqrt{25 + 1 + 4}$

$d = \sqrt{30}$

3. Final Answer

The length of the straw is $\sqrt{30}$ inches.