Question

If the rate of change of area of a square plate is equal to that of the rate of change of its perimeter, then length of the side is?

• A. $1$ unit
• B. $2$ unit
• C. $3$ unit
• D. $4$ unit

Answer 1

The correct option is B $2$ unit

Let at any time $t,$ the length of a side of the square be $x$. Then, $A=$ Area $=x^2$
and P$=$ Perimeter$=4x$
$\Rightarrow \frac{dA}{dt}=2x\frac{dx}{dt}$ and $\frac{dP}{dt}=4\frac{dx}{dt}$
It is given that $\frac{dA}{dt}=\frac{dP}{dt}$
$\Rightarrow 2x\frac{dx}{dt}=4\frac{dx}{dt}\Rightarrow x=2$.