Question

question
a straw is placed inside a rectangular box that is 6 inches by 3 inches by 8 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: Use space diagonal formula

The formula for the space diagonal $d$ of a rectangular prism with length $l$, width $w$, height $h$ is $d = \sqrt{l^2 + w^2 + h^2}$. Substitute $l=8$, $w=3$, $h=6$.
$$d = \sqrt{8^2 + 3^2 + 6^2}$$

Step2: Calculate squared terms

Compute each squared value and sum them.
$$d = \sqrt{64 + 9 + 36} = \sqrt{109}$$

Answer:

$\sqrt{109}$ inches