Fold corner A down to lie somewhere along side CD. Call x the portion of the way from C to D.
Corner B is outside of the original square and is now one side of a small triangle whose opposite side is along the remainder of side BC.
(A) Where would A be folded to make this small triangle isosceles?
(B) Find a formula in terms of x for the perimeter of this small triangle.
(C) Where would A be folded to maximize the area of this small triangle?