Greatest Area of a Rectangle
In the figure, OABC is a rectangle of perimeter 2l. Rectangle QEAB and QRSF are identical. OEFG is a square of perimeter 2l. Use the slider to change the value of l. Drag the point A to change the shape of rectangle OABC.
Since the area of rectangle OABC is equal to the sum of the area of rectangle OEQC and the area of rectangle QRSF, the area of rectangle OABC is alway less than the area of square OEFG. Therefore, as the shape of a rectangle varies, it becomes the largest when it is a square.