Question

The length $x$ of a rectangle is decreasing at the rate of $5cm/s$ and the width $y$ is increasing at the rate of $4cm/s$. When $x=10cm$ and $y=8cm$, then the area will

• A. remain same
• B. increase at the rate of $5c{m}^2/s$
• C. decrease at the rate of $5c{m}^2/s$
• D. data given is insufficient

Answer 1

The correct option is A remain same

Area of the rectange is
$A=xy\Rightarrow \frac{dA}{dt}=y\frac{dx}{dt}+x\frac{dy}{dt}\Rightarrow \frac{dA}{dt}=8\times (-5)+10\times \left(4\right)\Rightarrow \frac{dA}{dt}=0$
Hence, there is no change in area.