Minimizing the Length of a Fold: Solving a Calculus Problem

[heather_k2007]

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 so as to minimize the length of the fold? In other words, how would you choose x to minimize y?

Homework Equations

I know I need to use similar triangles and the Pythagorean Theorem (a^2+b^2=c^2) but I'm not sure of how to start the problem

The Attempt at a Solution

 

[Werg22]

You have to be more specif as for what you mean by the "length". There could be many interpretations.

 

[heather_k2007]

the length of the crease.

 

[Werg22]

Ok I get it. Well, say the hypotenuse of the triangle is y. The side along the bottom edge is x. The side along the vertical edge is z. Are you aware that

y + z = 12

?

 

[heather_k2007]

oh okay. i get that.

 

[heather_k2007]

i actually think i have it now. Thank you very much for your help!