shortest path

PRodQuanta

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

TenaliRaman

Some quick calculations give me .....
::I can get upto 12.70275561::
I don't think i can do better than that ....

-- AI

Janitor

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.

Gokul43201

I get [itex]\sqrt {(10 + 0.3 + 0.3)^2 + (3+4)^2}[/itex]

PRodQuanta

Gokul, how did you come to find this answer?

Paden Roder

NoTime

Read the equation.

Gokul43201

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.

Attached Images

linewall.bmp (9.0 KB, 231 views)