Create and complete the implementation of the Rectangle class. Your class should be public, not final and not abstract, inherit from the Shape class, and provide the following methods:

1. Constructor that takes two double parameters. Creates a new Rectangle with the passed width and height. You can assume that the passed parameters are greater than zero. You should call the Shape constructor and pass it the String "rectangle" to identify the type of this shape.
2. Public instance method area that takes no arguments and returns a double. Return the area of this shape: width * height.
3. Override public boolean equals(Object other). Return true if other is a Rectangle with the same width and height, and false otherwise. Note that other may be null or not a Rectangle.

Finally, note that your class should not expose any of its internal state publicly.