Explanation
To find the length of the longest rod that can be placed in the room, we need to calculate the length of the space diagonal of the rectangular room. This is the longest distance between any two points in a rectangular box.
Given the dimensions of the room are \(12\) meters, \(9\) meters, and \(8\) meters, the formula for the space diagonal \(d\) of a rectangular box with dimensions \(a\), \(b\), and \(c\) is:
\[
d = \sqrt{a^2 + b^2 + c^2}
\]
Here, \(a = 12\) meters, \(b = 9\) meters, and \(c = 8\) meters.
Calculate the space diagonal:
\[
d = \sqrt{12^2 + 9^2 + 8^2}
\]
\[
d = \sqrt{144 + 81 + 64}
\]
\[
d = \sqrt{289}
\]
\[
d = 17 \text{ meters}
\]
The length of the longest rod that can be placed in the room is 17 meters.
The correct answer is C. 17m.
