A straw is placed inside a rectangular box with dimensions 9 inches by 10 inches by 3 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 with dimensions 9 inches by 10 inches by 3 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

The length of the diagonal of a rectangular box with sides $a$, $b$, and $c$ is given by the formula:

$d = \sqrt{a^2 + b^2 + c^2}$

In this case, $a = 9$ inches, $b = 10$ inches, and $c = 3$ inches. Therefore, the length of the straw is:

$d = \sqrt{9^2 + 10^2 + 3^2}$

$d = \sqrt{81 + 100 + 9}$

$d = \sqrt{190}$

Since 190 = 2 * 5 * 19, there are no perfect square factors. Therefore, the simplified radical form is $\sqrt{190}$.

3. Final Answer

$\sqrt{190}$