Application of Rectangle Perimeter: Dynamic Exploration of Area Variation

This GeoGebra example dynamically demonstrates how the area of a rectangle changes when its perimeter is fixed, illustrating the classic optimization problem where the maximum area occurs for a square. Core mathematical concepts include perimeter and area formulas, functional relationships, and optimization. The construction uses the Polygon command to create rectangle ABCD, Segment and Vector commands for sides and auxiliary lines, an If command and sliders to control side lengths, and dynamic text (text1) to display current perimeter and area values. Suitable for middle and high school students to explore the relationship between perimeter and area, function graphs, and the concept of optimization in an interactive way.