There is a room 10 feet high by 10 feet wide by 10 feet in length. On one wall, there is an electrical outlet 1 foot from the floor and centered five feet from each side of the wall. On the opposite wall, one foot from the ceiling and centered five feet from each side of the wall, is an electrical box. How would you run a wire from the box to the outlet, attached to either the floor, ceiling or walls, that is less than 20 feet in length?
I have tried making a box to represent the room but can not figure out how the wire, running from box to outlet, could be less than 20 feet no matter how I run it.
Consider the room. The front wall is square ABCD, and the back wall is EFGH.
The front outlet (P) is a foot from the floor (AB), and the back outlet (Q) is a foot from the ceiling (GH).
A line directly up and across and down is 20 feet. But, you can do the following: Unfold the room and draw a new diagram, with
square ABCD
on its right is the wall BCFG
above that is the ceiling CGDH
to its right is the far wall, GHEF.
Now draw a line PQ. Its length is
√(16^2+10^2) = 18.86
I made your configuration with sheets of paper 10" x 10". I got the 16" leg, but I don't get the 10 foot height. I have the walls/ceiling in position similar to a backwards z. But from one foot over to the right from F, if I go straight up to form one of the legs, I get, up to G (one foot to the right), 9', plus 5' more to reach the box at Q, as it would have to travel half of the width of the wall. 9' + 5' =14', and the hypotenuse where the wire would lay would be slightly more than 21'. What am I looking at wrongly?
To determine how to run a wire from the electrical box to the outlet within the given constraints, we can break down the problem into simpler components. Let's consider the three possible routes to run the wire: along the floor, along the ceiling, or along the walls.
1. Along the floor:
To calculate the length of the wire needed for this route, we can add the three distances: from the box to the corner of the room, along the width of the room, and from the corner to the outlet. Let's calculate it step by step:
- Distance from the box to the corner of the room: Since the box is centered five feet from each side of the wall, the distance from the box to the adjacent corner can be calculated using the Pythagorean theorem:
sqrt(5^2 + 9^2) = sqrt(106) ≈ 10.3 feet (rounded to 1 decimal place).
- Distance along the width of the room: 10 feet.
- Distance from the corner to the outlet: Similar to the first step, we can use the Pythagorean theorem to calculate the distance from the corner to the outlet:
sqrt(5^2 + 9^2) = sqrt(106) ≈ 10.3 feet.
Now, adding up the three distances:
10.3 feet + 10 feet + 10.3 feet = 30.6 feet (rounded to 1 decimal place).
As we can see, running the wire along the floor exceeds the maximum allowed length of 20 feet.
2. Along the ceiling:
The process of calculating the wire length for this route is similar to the previous one. Again, we add the three distances: from the box to the corner of the room, along the width of the room, and from the corner to the outlet.
- Distance from the box to the corner of the room: 10.3 feet (as calculated before).
- Distance along the width of the room: 10 feet.
- Distance from the corner to the outlet: 10.3 feet (as calculated before).
Adding these three distances:
10.3 feet + 10 feet + 10.3 feet = 30.6 feet (rounded to 1 decimal place).
Once more, running the wire along the ceiling also exceeds the maximum allowed length of 20 feet.
3. Along the walls:
This routing option will require less wire since it avoids diagonally traversing the room.
- Distance along the width of the room: 10 feet.
- Distance along the height of the room (vertical drop): 10 feet.
- Distance along the length of the room: 10 feet.
Adding these three distances:
10 feet + 10 feet + 10 feet = 30 feet.
Even this route exceeds the maximum allowed length of 20 feet.
From the calculations, we can conclude that, given the dimensions of the room and the positions of the electrical box and outlet, there is no way to run a wire that is less than 20 feet in length within the given constraints.