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

The longest straight rod that can fit into a rectangular room equals the body (space) diagonal of the cuboid with dimensions 12 m × 9 m × 8 m. First compute the diagonal of the floor: √(12^2 + 9^2) = √225 = 15 m, then treat this as the base of a right triangle with height 8 m; the body diagonal is √(15^2 + 8^2) = √(225 + 64) = √289 = 17 m . Equivalently, apply the 3D diagonal formula directly: √(12^2 + 9^2 + 8^2) = √289 = 17 m . Hence option 3 (17 m) is correct.