Side of an equilateral triangle expands at the rate of 2 cm/sec. The rate of increase of its area when each side is 10 cm is

$10 \sqrt{3}$ cm²/sec

Let x be the side and A be the area of equilateral triangle at time t. Then,

$A=\frac{\sqrt{3}}{4} x^2$

$\Rightarrow \frac{d A}{d t}=\frac{\sqrt{3}}{2} x \frac{d x}{d t}$

$\Rightarrow \frac{d A}{d t}=\frac{\sqrt{3}}{2} \times 10 \times 2=10 \sqrt{3}$       [∵ x = 10 and $\frac{d x}{d t}$ = 2]