A rectangle is changing its length and width over time. (Note that it maintains its shape as a rectangle as these changes occur). Suppose that the length is decreasing at a steady rate of 2 centimeters per second and the width is increasing at a steady rate of 2 centimeters per second. At the moment when the length is 12 centimeters and the width is 5 centimeters: (a) What is the rate of change of the area of the rectangle? (b) What is the rate of change of the perimeter of the rectangle? (c) What is the rate of change in the length of the diagonals (i.e. lines that join opposite corners) of the rectangle?