Optimizaton-How would you fold a piece of paper to minimize the fold.?

Question

The upper right-hand corner of a piece of paper 12 by 8 is folded over to the bottom edge. How would you fold it to minimize the length of the fold? Basically, what are the dimensions of the fold. How far from the corner down, or how far from the corner to the left should the fold be made. The right corner is supposed to just touch the bottom edge.

This has to be done using calculus. Basically, the Pythagorean equation should be used here, c^2=a^2+b^2. We have to minimize c. So one of the variables has to be expressed in terms of 8, 12 and the other variable. I just can't find the relationship.

Answer 1

If the paper is 8 wide, match the top right hand corner with the bottom right hand corner. If the paper is 12 wide, match the top right hand corner with the bottom left hand corner.