Paper Folding Area Problem

[TajB]

Apologies if this is posted in the wrong category, if so I will happily relocate it.


Can an 8 by 12 piece of paper be folded in a manner shown below such that the trapezoidal region on the left has twice the area of the triangular region on the right? Determine the minimum and maximum values for the distance from the lower right corner of the paper to the point the corner touches the edge when folded as you still have a trapezoidal and triangular region. Plot the ratio of the two areas (Trapezoidal and Triangular) as the corner touching the edge moves from the minimum to maximum values.



I believe I have correctly related the variables, but the remainder of the problem has me stumped. Any help is greatly appreciated!

 

[Dr.Peterson]

One fact I don't think you have used is that the dotted line you drew on the top of the rectangle has length y. That will give you at least one more proportion to write.

 

[Jagulba]

ok few mistake that I can see

sqrt(16x-64) =4*sqrt(x-4) (you wrote 2 instead of 4)

"trapezoidal region on the left has twice the area of the triangular region "
this should be written like this
Atrap=2Atri
you wrote the opposite
2Atrap=Atri
take your time when do these things. I can see that you are smart enough to solve it why rush it