Answer:
Shortest length of wire = 28.60 feet
Step-by-step explanation:
<u>Distances In Rectangular Objects </u>
If we want to go from one point in space to another one, the shortest possible distance is through a line. But if we are not allowed to, we must try to use as many direct paths as possible to minimize the distance.
In our case, the minimum distance will be going right from one corner to the other through the air, but we must use walls and floor. So our choices are limited to shorten the distance as much as possible by taking paths from corners whenever it's possible.
Starting from the corner where the stereo system is located, we must try to reach the other corner by using one of these options
- Cross the floor by its diagonal and then go right to the other corner in the ceiling
- Cross one wall by its diagonal and then go to the other corner. It can be done for each adjacent wall to the stereo system.
If we try the first option first, the diagonal of the floor measures
And now we reach the other corner, traveling a total distance of
Trying one of the adjacent walls
And the final option is
We can see the first is the shortest distance, so to reach the speaker we must cross the floor by its diagonal and the go up to the speaker
Note: Each of the options analyzed have a identical counterpart by taking the opposite side first. For example, the path floor-wall could have been done as wall-ceiling, with identical results