Question

The length $x$ of a rectangle is decreasing at the rate of $5$cm/minute. When $x=8cm$ and $y=6cm$. Find the rate of change of
(i) the perimeter and
(ii) the area of rectangle

Answer 1

$P2(x+y)$
$A=xy$
$\frac{dx}{dt}=-50cm/min$
$\frac{dy}{dt}=4cm/min$
$\frac{dp}{dt}=2(\frac{dx}{dt}+\frac{dy}{dt})=2(-5+4)=-2cm/min$
Perimeter decreasing at $2cm/minute$
$\frac{dA}{dt}=x\frac{dx}{dt}+y\frac{dx}{dt}=8\left(4\right)+6(-5)=-32-30=2$
Area increasing at $2cm/min$