Area Variation of a Rectangle with Fixed Perimeter (Part 3)

This GeoGebra applet dynamically demonstrates how the area of a rectangle changes when its perimeter is kept constant. By interacting with the model to adjust the side lengths, users can visually observe the impact of the length-to-width ratio on the area under a fixed perimeter constraint. Combining geometric construction with algebraic calculation, this model helps explore the maximum area problem for rectangles and intuitively verifies related mathematical inequality properties, making it an excellent interactive teaching tool for studying plane geometry and optimization of extreme values. Users can drag the endpoints of the rectangle's sides to change its dimensions while the perimeter remains unchanged. As the length and width vary, the applet updates the displayed area in real time, allowing students to discover that the area is maximized when the rectangle becomes a square. The applet also illustrates the arithmetic mean-geometric mean inequality in a geometric context, showing that for any rectangle with fixed perimeter, the square always yields the largest possible area. This visual and hands-on approach deepens conceptual understanding and supports inquiry-based learning in secondary mathematics classrooms.