What is the Shortest Cord Length for Clock to Outlet?

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Discussion Overview

The discussion revolves around determining the shortest length of an extension cord needed to connect a clock mounted on one wall of a room to an outlet on the opposite wall, while adhering to the constraint that the cord must touch the walls, floor, or ceiling at all times. The problem involves geometric reasoning and calculations related to the dimensions of the room.

Discussion Character

  • Mathematical reasoning
  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant describes the room's dimensions and the positions of the clock and outlet, outlining the need for the shortest cord length.
  • Another participant provides a calculated length of approximately 12.70275561 feet, suggesting this may be the optimal solution.
  • A different approach is proposed, where participants suggest visualizing the problem by unfolding the walls, floor, and ceiling to create a flat representation for easier calculation.
  • One participant presents a mathematical expression involving the square root to derive a potential solution, indicating a geometric approach to the problem.
  • Questions are raised about the reasoning behind the calculations, with requests for clarification on how specific answers were derived.
  • Another participant emphasizes the importance of knowing the correct way to unfold the paper model, indicating that multiple unfolding methods may exist.

Areas of Agreement / Disagreement

Participants appear to explore various methods for solving the problem, with some calculations and approaches presented. However, there is no consensus on a single solution, and multiple viewpoints regarding the unfolding technique and calculations remain evident.

Contextual Notes

The discussion includes various assumptions about the unfolding technique and the geometric interpretation of the problem. There may be limitations in the assumptions made regarding the layout and the potential for different configurations that could affect the calculations.

PRodQuanta
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Picture a room (a rectangular prism) that is 10 feet long x 4 feet wide x 3 feet high. Now, in the middle of the 4 foot wall, .3 feet down from the top, there is a clock. On the opposite wall, .3 foot from the bottom, there is an outlet.

So... I want the shortest length for the extension cord from the clock that is .3 feet from the top to the plug in that is .3 from the bottom.

The cord must be touching a wall at all times (it must be taped to the wall) (or the floor or ceiling.)

i.e.-If you went in a straight line. You would go 2.7 feet down, 10 foot across, and .3 feet up, for a grand total of 13 foot.

There is another way to get a shorter distance.

Paden Roder
 
Last edited:
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Some quick calculations give me ...
::I can get upto 12.70275561[/Color]::
I don't think i can do better than that ...

-- AI
 
I have seen this sort of problem before. The solution can be found by imagining the walls/floor/ceiling to be made of folded paper, and mentally unfolding them to make them flat, then drawing a straight line from point A to point B.
 
I get [itex]\sqrt {(10 + 0.3 + 0.3)^2 + (3+4)^2}[/itex]
 
Gokul, how did you come to find this answer?

Paden Roder
 
PRodQuanta said:
Gokul, how did you come to find this answer?

Paden Roder

Read the equation. :smile:
 
PRodQuanta said:
Gokul, how did you come to find this answer?

Paden Roder

Basically, you do what Janitor said...only you have to know the right way to unfold the paper model, for there are many possibilities. Looks like Tenali got this first, and my number is the same as his...so I'm thinking it's probably the right one.

see picture in attachment.
 

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