The length x of a rectangle is decreasing at the rate of 2 cm/minute and the width y is decreasing at the rate of 3 cm/minute. When x =10cm and y = 10 cm, find the rates of change of the perimeter of the rectangle.
Answer & explanation
Correct answer: option 4
Perimeter of Rectangle, $P=2(x+y)$
$⇒\frac{dp}{dt}=2\left(\frac{dx}{dt}+\frac{dy}{dt}\right)$
$⇒\frac{dp}{dt}=2(-2-3)$
$⇒\frac{dp}{dt}=2×-5=-10\,cm/min$