A stereo system is being installed in a room with a rectangular floor measuring 13 feet by 11 feet and a 7-foot ceiling. The st
ereo 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.)
1 answer:
Answer:
about 22.2 feet
Step-by-step explanation:
The wire can run diagonally across the floor and, from the intersection with the wall, diagonally up the wall. The total length is computed per the hint to be ...
d = √(18^2 +13^2) = √493 ≈ 22.20 . . . . feet
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If the wire were to go up the short wall, its length would be ...
d = √(11^2 +20^2) = √521 ≈ 22.83 . . . . feet
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<em>Comment on the attachment</em>
The red represents the floor; the green represents the long wall.
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