Question

question
a straw is placed inside a rectangular box that is 7 inches by 9 inches by 9 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.
answer attempt 1 out of 2

Explanation:

Step1: Recall space diagonal formula

For a rectangular prism with side lengths $l, w, h$, the space diagonal $d$ is $d = \sqrt{l^2 + w^2 + h^2}$

Step2: Substitute given values

Here $l=9$, $w=9$, $h=7$. Substitute into formula:
$d = \sqrt{9^2 + 9^2 + 7^2}$

Step3: Calculate squared terms

Compute each squared value:
$d = \sqrt{81 + 81 + 49}$

Step4: Sum the terms inside root

Add the values:
$d = \sqrt{211}$

Answer:

$\sqrt{211}$ inches