Minimizing Length of a Crease

I have been working on this problem for a while now, i have nailed the other 2 cases possible for this problem but the last case has me stuck

here is the problem

** You have a sheet of paper that is 6 units wide and 25 units long placed**

so that the short side is facing you. Fold the lower right hand corner

over to touch the left side. Your task is to fold the paper in such a way

that the length of the crease is minimized. What is the length of the

crease?

Do with without using trigonometry

currently i am working on the case on the far right (i have completed the first two)

http://euclid.trentu.ca/math/courses...998/sheets.gif

This is the diagram that i have made.

http://i42.photobucket.com/albums/e3...tled-2copy.jpg

Everything that is not in computer font was what i originally had drawn myself. The computer additions are what my teacher added to my diagram, all of which have confused me even more.

My professor has told me that i have to relate L (length of the crease) in terms of x. He has also given me A which he says i will needed. I dont know how these variables relate or how to start this problem

If any more diagrams are needed i will provide them on request

This is urgent i need to turn this in asap

Thanks for taking your time to look and help me

1 Attachment(s)

Re: Minimizing Length of a Crease

Only in case it isn't quite clear which geometric properties I used I've attached a more detailed sketch.

Prove that the angles marked in orange are equal. Show that the grey triangle is isesceles because the base angles at the red base are equal.