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
Answer & explanation
Correct answer: option 2
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]