Rectangles: Perimeter vs Area — Maximum Area Demo

This GeoGebra example demonstrates how the area of a rectangle changes under a fixed perimeter constraint, highlighting the configuration that yields the maximum possible area. It connects the geometric setting with the algebraic structure A = ab and P = 2(a+b), turning the constraint into a product-based relationship. The construction emphasizes optimization under constraint and the characteristic curve behavior linked to products and root/hyperbola-like relationships. Build-wise, it uses Intersect to locate key intersection points, PointIn to determine whether points lie inside the relevant polygon region, Polygon to draw the rectangle and auxiliary shapes, and Midpoint plus Centroid to define symmetric/central reference points for labeling and structure. Interactive objects (e.g., A, B, q1, a, b, together with helper objects like f, g, o) and UI elements (button1, text1–text6) guide the visualization toward the maximum-area result. Suitable for high-school advanced geometry/algebra and early university optimization/graphing lessons.