Maximize the Area of a Rectangle with Fixed Perimeter

This GeoGebra example demonstrates how the area of a rectangle changes when its perimeter is kept constant, and visually shows that the maximum area occurs when the rectangle becomes a square. The core mathematical concepts include the formulas for perimeter and area of a rectangle, quadratic functions, finding extrema via derivatives, and basic optimization. The construction uses GeoGebra commands such as Point, Segment, OrthogonalLine, Circle, Intersect, Polygon, and Text to build the rectangle and its auxiliary elements, with sliders or draggable points to vary side lengths. Dynamic text displays the current area and perimeter values, and a graph of area versus side length (likely a parabola) is shown to illustrate the maximum. This resource is suitable for middle and high school mathematics classes, particularly for teaching quadratic function maxima, derivative applications, or geometric optimization problems, and can be used for guided inquiry or demonstration.