Question

a straw is placed inside a rectangular box that is 5 inches by 2 inches by 10 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.

Explanation:

Step1: Recall space diagonal formula

The space diagonal $d$ of a rectangular prism with length $l$, width $w$, height $h$ is given by:
$$d = \sqrt{l^2 + w^2 + h^2}$$

Step2: Substitute given values

Here, $l=10$ in, $w=5$ in, $h=2$ in. Substitute into the formula:
$$d = \sqrt{10^2 + 5^2 + 2^2}$$

Step3: Calculate squared terms

Compute each squared value:
$$d = \sqrt{100 + 25 + 4}$$

Step4: Sum and simplify radical

Add the terms inside the radical:
$$d = \sqrt{129}$$

Answer:

$\sqrt{129}$ inches