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A stereo system is being installed in a room with a rectangular floor measuring 13 feet by 10 feet and a 9​-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?

(Hint: Turn the problem into an equivalent simpler problem by imagining cutting the room along its vertical corners and unfolding it so that it is flat. You will be able to apply the Pythagorean​ theorem.)
The shortest length of wire that can be used is _____ ft.

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Answer:

The shortest length of wire that can be used is _25.4_ ft.

Step-by-step explanation:

To solve this problem we can follow the following steps:

1) We have the dimensions of the floor of the room. The shortest distance between its opposite corners is the diagonal. We calculate the diagonal using the Pythagorean theorem.

[tex]a = \sqrt {13 ^ 2 + 10 ^ 2}[/tex]

[tex]a = 16.40\ ft.[/tex]

2) Since the speaker is on the ceiling, and the amplifier is on the floor, then 9 more feet of cable is needed to reach the speaker.

3) The final distance (d) is:

[tex]d = 16.40\ ft + 9\ ft\\d = 25.4\ ft.[/tex]

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