Question

Each side of an equilateral triangle is increasing at the rate of 8 cm/hr. The rate of increase of its area when side is 2 cm, is

पर्याय

• \[8\sqrt{3} \ {cm}^2 /hr\]

• \[4\sqrt{3} \ {cm}^2 /hr\]

• \[\frac{\sqrt{3}}{8} \ {cm}^2 /hr\]

• none of these

Answer 1

 \[8\sqrt{3} \ {cm}^2 /hr\]

\[\text { Let x be the side and A be the area of the equilateral triangle at any time t. Then },\]

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

\[ \Rightarrow \frac{dA}{dt} = \frac{\sqrt{3}}{2}x\left( \frac{dx}{dt} \right)\]

\[ \Rightarrow \frac{dA}{dt} = \frac{\sqrt{3}}{2}\left( 2 \right)\left( 8 \right)\]

\[ \Rightarrow \frac{dA}{dt} = 8\sqrt{3} \ {cm}^2 /hr\]