While measuring the side of an equilateral triangle an error of $k \%$ is made, the percentage error in its area, is

Let $x$ be the length of a side of the triangle. Then,
its area $A$ is given by

$A=\frac{\sqrt{3}}{4}{x}^2\Rightarrow \frac{dA}{dx}=\frac{\sqrt{3}}{2}x$

$\begin{array}{l}\therefore \mathrm{\Delta }A=\frac{dA}{dx}\mathrm{\Delta }x\\ \Rightarrow \mathrm{\Delta }A=\frac{\sqrt{3}}{2}x\mathrm{\Delta }x\\ \Rightarrow \frac{\mathrm{\Delta }A}{A}\times 100=\frac{{\displaystyle \frac{\sqrt{3}}{2}}x∆x}{\frac{\sqrt{3}}{4}{x}^2}\times 100=2\left(\frac{\mathrm{\Delta }x}{x}\times 100\right)=2k\end{array}$