Question

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

Options

• \[10\sqrt{2} \ {cm}^2 /\sec\]

• \[10\sqrt{3} {cm}^2 /\sec\]

• 10 cm²/sec
  
  

• 5 cm²/sec

Answer 1

\[10\sqrt{3} \ {cm}^2 /\sec\]

\[\text { Letxbe the side andAbe the area of the equilateral triangle at any timet.Then },\]
\[A = \frac{\sqrt{3}}{4} x^2 \]
\[ \Rightarrow \frac{dA}{dt} = 2 \times \frac{\sqrt{3}}{4} x^{} \frac{dx}{dt}\]
\[\Rightarrow\frac{dA}{dt}=\frac{\sqrt{3}}{2}\times2\times10\]
\[\Rightarrow\frac{dA}{dt}=10\sqrt{3} \ {cm}^2 /sec\]