Question

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. How far is the area increasing when the side is 10 cms?

Answer 1

$$\begin{gathered} \text{Let}\mathit{\text{x}}\text{be the side and}\mathit{\text{A}}\text{be the area of the equilateral triangle at any time}\mathit{\text{t.}}\text{Then,} \\ A=\frac{\sqrt{3}}{4}{\mathit{\text{x}}}^2 \\ \Rightarrow \frac{dA}{dt}=2\times \frac{\sqrt{3}}{4}{\mathit{\text{x}}}^{}\frac{dx}{dt} \\ \text{⇒}\frac{dA}{dt}\text{=}\frac{\sqrt{3}}{2}\text{×2×10} \\ \text{⇒}\frac{dA}{dt}\text{=10}\sqrt{3}{\text{cm}}^2\text{/sec} \end{gathered}$$