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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Comment on the attachment
The red represents the floor; the green represents the long wall.
The shortest length of wire between the stereo system and speaker opposite site of wall connection is 22.2 feet.
The shortest distance of the rectangular plane is the length of the diagonal of the rectangle.
The diagonal of the rectangle can be find using the following formula.
[tex]d=\sqrt{l^2+w^2}[/tex]
Here, (l) is the length of the rectangle and (w) is the width of the rectangle.
Given information-
The dimensions of the rectangular floor is 13 feet by 11 feet and a 7-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.
The wire must run along the floor or walls.
To select the shortest length of the wire, which should be required to connect the stereo amplifier to the speaker must go diagonally from the floor to the wall.
The width of the wall is 11 feet and the celling is 7 foot. Thus the total length of the rectangle which is made by the wire as a diagonal is 18 foot.
Width of the rectangle equal to the length of the floor which is 13 feet.
Thus the shortest distance or diagonal is,
[tex]d=\sqrt{18^2+13^2}\\d=22.2\rm ft[/tex]
Thus the shortest length of wire you can use for the connection is 22.2 feet.
Learn more about the diagonal of the rectangle here;
https://brainly.com/question/17117320
