A stereo system is being installed in a room with a rectangular floor measuring 16 feet by 12 feet and an 8-foot ceiling. The stereo amplifier is on the floor in one corner of the room. A speaker is at the ceiling in the opposite corner of the room. You must run a wire from the amplifier to the speaker, and the wire must run along the floor or walls (not through the air). What is the shortest length of wire you can use for the connection?
Accepted Solution
A:
Answer: 4√41 ≈ 25.61 feetStep-by-step explanation:The shortest route is the one that crosses the longest edge between room surfaces. In this case, that is the 16-foot edge between the floor and wall opposite the amplifier, or the 16-foot edge between the ceiling and the wall adjacent to the amplifier.The length of the required wire is ... √((8+12)² +16²) = √656 = 4√41 ≈ 25.61 . . . feet