Area and Perimeter of Rectangle with Fixed Perimeter

① This example demonstrates how the area of a rectangle changes with its side lengths when the perimeter is fixed, showing that the maximum area occurs when the rectangle is a square. ② Core mathematical concepts include the area and perimeter formulas for rectangles, quadratic functions, optimization (finding maximum), and variable dependency. ③ Construction highlights: sliders (a, b) control side lengths; Point, Line, and Polygon construct the rectangle; Area command computes area; Distance measures sides; DynamicCoordinates updates positions; Textfield and InputBox allow interactive input; OrthogonalLine and Intersect help build perpendicular relations; Midpoint marks centers; VerticalText and Text display labels; Div performs division; a button may reset or trigger calculations. ④ Suitable for middle school to high school students learning geometry and algebra, useful for exploring quadratic maxima, rectangle properties, and dynamic math experiments.