Peter made a paper rectangle, put it on an identical rectangle and pasted both rectangles along their perimeters. Then he cut the upper rectangle along one of its diagonals and along the perpendiculars to this diagonal from two remaining
vertices. After this he turned back the obtained triangles in such a way that they, along with the lower rectangle form a new rectangle.
Let this new rectangle be given. Restore the original rectangle using compass and ruler.
Get the midpoints of (the two shorter sides of) the new rectangle and connect them. This is a diagonal of the original rectangle. Now, draw the circle with this diagonal as a diameter. The two points it intersects the new rectangle will be the other two vertices of the original rectangle (it actually intersects in 4 points, but disregard one pair of opposite points).