Why the sketch works: [br]This sketch works because the perimeter is AB, which is 8.7 and remains constant. The length and the width change when you move point C. The circle creates a segment that is congruent to AC. The midpoint D defines the last two segments CD and DB and ensures that they are also congruent. [br][br]What the graph shows:[br]Essentially, point G has the coordinates of AC and the area of polygon 1. It is traced to show all of the possible values for AC. We can see that a parabola is formed and the maximum occurs when the length equals the width. After that, one increases as the other decreases and vice versa. I can also see that the length equals the width because the two circles creating and length and the width align. [br]