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=8` cm and `y=6` cm , find the rate of change of (a) the perimeter, (b) the area of the rectangle.

Explanation

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

### Given Information:
- Length of the rectangle, \( x \) (decreasing) = 8 cm
- Width of the rectangle, \( y \) (increasing) = 6 cm
- Rate of change of length, \( \frac{dx}{dt} = -5 \) cm/min (negative because it is decreasing)
- Rate of change of width, \( \frac{dy}{dt} = 4 \) cm/min (positive because it is increasing)

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