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=8c m` and `y=6,` find the rates of change of (i) the perimeter (ii) the area of the rectangle.

Explanation

Since the length `(x)` is decreasing at the rate of `5cm` / minute and the width

`(y)` is increasing at the rate of `4 cm`/ minute, we have:

`frac{d x}{d t}=-5 cm}`/ min and `frac{d y}{d t}=4 cm` / min
(a) The perimeter (P) af a rectangle is given by,

`P=2(x+y)`

therefore `frac{d P}{d t}=2(frac{d x}{d t}+frac{d y}{d t})=2(-5+4)=-2 cm` / min

Hence, the perimeter is decreasing at the rate of `2 cm` / min.

(b) The area (A) of a rectangle is giyen by,

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