Question

a shipping container in the shape of a rectangular prism is 36 inches long, 27 inches wide, and 15 inches high. to the nearest tenth of an inch, what is the length of the longest rod that can fit inside the container? inches

Explanation:

Step1: Recall the space - diagonal formula

The length of the space - diagonal $d$ of a rectangular prism with length $l$, width $w$, and height $h$ is given by the formula $d=\sqrt{l^{2}+w^{2}+h^{2}}$.
Here, $l = 36$ inches, $w = 27$ inches, and $h = 15$ inches.

Step2: Calculate $l^{2}+w^{2}+h^{2}$

$l^{2}=36^{2}=1296$, $w^{2}=27^{2}=729$, $h^{2}=15^{2}=225$.
$l^{2}+w^{2}+h^{2}=1296 + 729+225=2250$.

Step3: Find the length of the space - diagonal

$d=\sqrt{2250}\approx47.4$ inches.

Answer:

$47.4$