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 units
• C. 3 units
• D. 4 units

Answer 1

Answer: (B)

2 units

Area of square $A=x^2$

$\frac{dA}{dt}=2x\frac{dx}{dt}$

Perimeter of square $P=4l$

$\frac{dP}{dt}=4\frac{dl}{dt}$

Since, $\frac{dA}{dt}=\frac{dP}{dt}$

$\Rightarrow (2x-4)\frac{dx}{dt}=0$

$\Rightarrow 2x-4=0$

$\Rightarrow x=2$ units