Rectangles in the {Perimeter, Area} plane

The right panel is a {width, height} plane}. Every point in the first quadrant of this plane corresponds to a rectangle. [br][br]The applet allows you to generate either a family of rectangles by moving the GOLD point along a [br][b][i]height = constant/width[/i][/b] curve or a family of rectangles by moving a GOLD point along a [br][b][i]height+width = constant[/i][/b] curve.[br][br][[size=85][b][i]You can position each of these curves by dragging the small WHITE dots.[/i][/b][/size]][br][br]Can you explain the nature of the curves generated in the left panel [the {Perimeter, Area} plane] as you drag the GOLD dots in the {width, height} plane? qualitatively? analytically?[br][br]What have you learned from this applet?[br][br][b][i][color=#ff0000]What questions would/could you put to your students based on this applet?[br][/color][/i][/b][br]

Information: Rectangles in the {Perimeter, Area} plane