If a rectangle has a fixed perimeter, find for what dimensions the rectangle will have maximum area.[br][list][br][*]Change the shape of the rectangle by moving the blue point.[br][*]The red point in the first quadrant has x-coordinate equal to one side of the rectangle and y-coordinate equal to the area of the rectangle. Observe the way the point is moving to find when the rectangle will have maximum area.[br][*]Show the locus of the point.[br][*]Find the function that will describe the area as a function of one side of the rectangle and enter it in the input box. Hit Enter to graph it.[br][br][/list]