Inscribed Rectangle in a Triangle: Quadratic Function Model

①This example demonstrates how to construct a rectangle inscribed in an arbitrary triangle and observe how its area changes as the rectangle's position varies, revealing a quadratic relationship between area and position. ②Core math concepts include quadratic functions, optimization (maximizing area), geometric constraints (rectangle vertices lying on triangle sides), and function modeling. ③Construction details: using GeoGebra commands such as Intersect to find points, Polygon to create the triangle, Point for dynamic vertices, OrthogonalLine to ensure perpendicularity, Segment for edges, Extremum to locate the maximum of the area function, and Textfield/InputBox1 for interactive input, ultimately producing a graph of the area as a quadratic function of the rectangle's position. ④Suitable for high school students learning quadratic functions, connecting geometry with algebra, or for mathematical modeling activities to illustrate how geometric problems translate into function optimization.