Her rectangle problem is wrong. Here are four rectangles with the same area and perimeter:

x = 3, y = 6; x = 4, y = 4; x = 5, y = 10/3; x = 7, y = 14/5

The formula is fix x > 2 (one side), let y = 2x / (x-2) (other side). Derived from xy = 2x + 2y.