The sides of an equilateral triangle are increasing at the rate of 2…

The correct answer is Option (2) → \(10\sqrt{3}\) cm²/sec

Let the side be x cm. The area of an equilateral triangle is

    \( \displaystyle A = \frac{\sqrt{3}}{4}x^2 \)

Differentiating with respect to time t (rate of change):

    \( \displaystyle \frac{dA}{dt} = \frac{\sqrt{3}}{4} \cdot 2x\frac{dx}{dt} = \frac{\sqrt{3}}{2}\,x\frac{dx}{dt} \)

Putting \(x = 10\) and \(\frac{dx}{dt} = 2\):

    \( \displaystyle \frac{dA}{dt} = \frac{\sqrt{3}}{2} \times 10 \times 2 = 10\sqrt{3} \) cm²/sec

NCERT Exemplar:
Application of Derivatives