Optimization problem: Folding a triangle to minimize one side

[PsychStudent]

Homework Statement

The upper right-hand corner of a piece of paper, 12 in by 8 in is folded over to the bottom edge. How would you fold it to minimize the length of the fold? In other words, how would you choose x to minimize y?

Homework Equations

None so far.

The Attempt at a Solution

I haven't a clue how to get started. I know I need to relate the length of y to the length of x and then differentiate and find the minima, but I don't know how to form the initial relationship.

 

[berkeman]

Hint -- use the 8x12" information as part of the equations your write. If x is as shown, then the bottom piece is 8-x, right? What can you say about the angles in the two triangles that are formed by that fold?