The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8cm and y = 6cm, find the rates of change of (a) the perimeter, and (b) the area of the rectangle

Explanation

To solve the problem step by step, we will find the rates of change of the perimeter and the area of the rectangle based on the given rates of change of length and width.

### Given:
- The length \( x \) of the rectangle is decreasing at a rate of \( \frac{dx}{dt} = -5 \) cm/min (negative because it is decreasing).
- The width \( y \) of the rectangle is increasing at a rate of \( \frac{dy}{dt} = 4 \) cm/min.
- At the moment of interest, \( x = 8 \) cm and \( y = 6 \) cm.

### Part (a): Rate of Change of the Perimeter
...