A rectangular box has dimensions 1 inch by 3 inches by 5 inches. A straw fits exactly along the diagonal from the bottom left corner to the top right back corner. We need to find the length of the straw.

1. Problem Description

A rectangular box has dimensions 1 inch by 3 inches by 5 inches. A straw fits exactly along the diagonal 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, $d$, of a rectangular box with dimensions $l$, $w$, and $h$ is given by the formula

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

In this case, $l = 1$ inch, $w = 3$ inches, and $h = 5$ inches. Substituting these values into the formula, we get:

$d = \sqrt{1^2 + 3^2 + 5^2}$

$d = \sqrt{1 + 9 + 25}$

$d = \sqrt{35}$

Since 35 has no perfect square factors other than 1, the radical $\sqrt{35}$ is in simplest form.

3. Final Answer

$\sqrt{35}$ inches