how would you choose x to minimize y ( PLease help as soon as possible i cant find the answer)?

Question

The upper right-hand corner of a piece of paper, 60in. by 32 in., is folded over to the bottom

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?

the answer should be in inches

Answer 1

You got a good problem there. Let me try and get you going. This was actually set up on an 8-1/2 x 11 page. Let length(AB) or L(AB), where A is the start of the fold on the 60 inch side and B is the corner on the right=upper side be x. Let L(BC)= z, where C is the start of the fold on the 32 inch side. Draw triangle ACD, where D is where the fold just touches the bottom of the page. Let E be the bottom corner of the piece. Then CDE is a triangle with height 32-z, hypotenuse z and angle CDE = arcsin[(32-z)/z]. Call this angle theta. Now draw the altitude from D to the other long side, which intersects that side at F. Now L(DF)= 32, angle ADF is theta and L(AD)= 32/Cos(theta). Now, the length of the fold =
sqrt(L(AD)^2+ z^2). This is what we want to minimize. AD is a function of theta, which is a function of z through the arcsin relation. The final function you have to take the derivitive of may be messy. But good luck if you choose to take it on.

Answer 2

fold it to the lower right hand corner

Answer 3

i found x= 56/sqrt(3) and y=(56/3).sqrt(7) . the solution is really hard to write here. find a relation between angles and take derivative.