The length x of a rectangle is decreasing at the rate of 10 cm/minute and the width y is decreasing at the rate of 10 cm/minute. Then which of the following is true regarding the rate of change of area and the rate of change of perimeter when x=2 cm and y = 2cm.
Answer & explanation
Correct answer: option 2
A = x.y
P = 2(x+y)
$\frac{dA}{dt} = x\frac{dy}{dt} + y\frac{dx}{dt} = 2\times -10 + 2\times -10 = -40 cm^2/minutes$
$\frac{dP}{dt} = 2(\frac{dx}{dt} + \frac{dy}{dt}) = -40 cm/minutes$
$\Rightarrow \frac{dA}{dt} = \frac{dP}{dt}$
Both decreases at the same rate.