The length of the longest pole that can be placed in a room 12 m long and 9 m wide and 8 m high is

To find the length of the longest pole that can fit in a rectangular room, we need to calculate the length of the space diagonal. The formula for the space diagonal of a cuboid is the square root of the sum of the squares of its length, width, and height. First, square each dimension: 12 squared is 144. 9 squared is 81. 8 squared is 64. Next, add these values together: 144 plus 81 plus 64 equals 289. Finally, take the square root of 289. The square root of 289 is 17. Therefore, the length of the longest pole is 17 m. The correct option is C.