The upper right-hand corner of a piece of paper, in. by in., as in the figure, is folded over to the bottom?

Question

The upper right-hand corner of a piece of paper, in. by in., as in the figure, is folded over to the bottom edge. How would you fold it so as to minimize the length of the fold? In other words, how would you choose x to minimize Y?

Answer 1

Intuitively, you would fold it so the top right corner was touching the bottom right corner. This gives you a length of fold of W. Any other fold length will be longer.