Optimizing Crease Length for a Folded Sheet of Paper

[fadi_nzr]

You have a sheet of paper that is 6 units wide and 25 units long placed
so that the short side is facing you. Fold the lower right hand corner
over to touch the left side. Your task is to fold the paper in such a way
that the length of the crease is minimized. What is the length of the
crease?

this what I have attempted so far

by proportions we get:

b/20 = a/sqrt(12a-36)

Solving for b. Use Pythagorean theorem to determine the length of c:

c^2 = a^2 + (36a^2)/(12a-36)

I am not sure if I am in the right track or not

any ideas or corrections

 

[haruspex]

Your diagram seems to assume the crease will go through the top right hand corner. Why should that produce the minimum length?

 

[fadi_nzr]

so how it should be

 

[mfb]

Let it go through some arbitrary other point. And try to make the sketch a bit more realistic in terms of the length ratio (6:25).