Consider the following data-type implementation for axis-aligned rectangles, which represents each rectangle with the coordinates of its center point and its width and height: Write an API for this...

Consider the following data-type implementation for axis-aligned rectangles, which represents each rectangle with the coordinates of its center point and its width and height:

Write an API for this class, and fill in the code for perimeter(), intersects(), and contains(). Note: Consider two rectangles to intersect if they share one or more common points (improper intersections). For example, a.intersects(a) and a.contains(a) are both true.