Changing dimensions in a rectangle is decreasing at the rate of 2 $\mathrm{cm} / \mathrm{sec}$ while the width $w$ is increasing at the rate of 2 $\mathrm{cm} / \mathrm{sec} .$ When $l=12 \mathrm{cm}$ and $w=5 \mathrm{cm},$ find the rates of change of (a) the area, (b) the perimeter, and (c) the lengths of the diagonals of the rectangle. Which of these quantities are decreasing, and which are increasing?