Equable Rectangles Finder: Constructing rectangles from area–perimeter constrain

This GeoGebra example demonstrates how to find and construct “equable” rectangles, where the rectangle’s dimensions satisfy a given relationship involving area and perimeter (or an equivalent equability condition). It highlights the geometric phenomenon that valid rectangles correspond to specific intersection/constraint solutions, and it visualizes how length and width are determined. Key math concepts include rectangle area and perimeter, rational-number relationships, and using a tangent function to encode the required constraint. Construction approach: Intersect and Point locate and define critical solution points; Segment and Polygon build the rectangle edges and the filled shape; OrthogonalLine ensures right angles and proper auxiliary lines; RotateText is used for readable rotated labels tied to parameters and computed values. Suitable for late secondary school through early university, especially for geometry construction, function/constraint-based modeling, and guided problem solving.