Question

The length x of a rectangle is decreasing at the rate of 3 cm/minute and the width y is increasing at the rate of 2 cm/minute, when x = 10 cm and y = 6 cm, find the rates of change of the perimeter.

Answer 1

Let P be the perimeter of rectangle.

P = 2(x+y)

Differentiating w.r.t. 't' we get

= - 2 cm/minute.

⇒ Perimeter of rectangle is decreasing at the rate of 2 cm/minute.