To find the length of the longest rod that can fit inside the shipping container, we need to calculate the length of the diagonal of the rectangular prism. The formula for the diagonal \( d \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
Given:
- Length \( l = 36 \) inches
- Width \( w = 27 \) inches
- Height \( h = 15 \) inches
Now, we can plug in the values:
\[ d = \sqrt{36^2 + 27^2 + 15^2} \]
Calculating each square:
- \( 36^2 = 1296 \)
- \( 27^2 = 729 \)
- \( 15^2 = 225 \)
Now add them together:
\[ 1296 + 729 + 225 = 2250 \]
Now take the square root of 2250:
\[ d = \sqrt{2250} \approx 47.4341649 \]
Finally, rounding to the nearest tenth of an inch:
\[ d \approx 47.4 \text{ inches} \]
Thus, the length of the longest rod that can fit inside the container is approximately 47.4 inches.
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