A very long rectangular piece of paper is 20 cm wide. The bottom right hand corner is folded along the crease so that the corner just touches the left hand side of the page. How should the page be folded to make the crease as short as possible?
I know that I must use Pythagorean theorem. But, since this is in the trig function chapter I can assume that I'll probably have to use a trig function.
Okay, 20 cm side is "a" side. Crease side (hypotenuse) is "c." And, the remaining side will be "b." c=sqrt[(20-a)^2+b^2]. I know that the Domain for "a" must be 0<a=<20. I also know that as "a" gets closer to 20 "c" gets smaller. Its all well and good that I know the answer must be 20 but I don't get points for observations. Anyhow, knowing that the answer must be a=20 then I know that the angle created by turning the page will be 90 degrees.
I know all this but I don't know how to make the constraint with this information. How do I turn my objective function into a single variable function?
Thanks for the help.