Is this possible physically? The length $x$ of a rectangle is decreasing at the rate of $5 \, cm/min$ and the width $y$ is increasing at the rate of $4\, cm/min$. When $x=8\, cm$ and $y=6 \,cm$, find the rates of change of 
(a) the perimeter and  (b) the area of rectangle.
$$ \frac{dx}{dt} =-5\,\,cm/min, \, \frac{dy}{dt} =4\,\, cm/min$$
(a) $\frac{dP}{dt} =-2\, cm/min$ (perimeter decreases at the rate of $2\, cm/sec$)
(b) $\frac{dA}{dt} = 2 \, cm^2/sec$ (area of the rectangle is increasing at the rate of $2 \,cm^2 /min$)
Now I ask that is this possible in the physical sense?

So the question is:

Can the perimeter decrease and the area increase?

Absolutely. Consider a rectangle with sides 3 and 4. It has area 12 and perimeter 14.
Now make the short side a bit longer and the long side a bit shorter, we get a new rectangle with sides (for example) 3.1 and 3.89. It has a larger area $$3.1 \cdot 3.89 = 12.059 > 12$$but a shorter perimeter $$2 \cdot 3.1 + 2 \cdot 3.89 = 13.98 < 14$$
