The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when side is 10 cm is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $10\sqrt{3}cm^2/s$
Let the side of the equilateral triangle be $x$ cm.
Area = $\frac{\sqrt{3}}{4}x^2$
$⇒\frac{dA}{dt}=\frac{\sqrt{3}}{4}×2x×2$
Now,
$\left.\frac{dA}{dt}\right|_{x=10}=\frac{\sqrt{3}}{4}×2×10×2=10\sqrt{3}cm^2/s$