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Lapatulllka [165]
3 years ago
7

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 s

tereo 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?

Mathematics
1 answer:
Snezhnost [94]3 years ago
8 0

Answer:

  4√41 ≈ 25.61 feet

Step-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

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