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

(b) 2k%

Let x be the side of the triangle and y be its area.

$\frac{\Delta x}{x} \times 100=k$

Also, $y=\frac{\sqrt{3}}{4} x^{2}$

$\Rightarrow \frac{d y}{d x}=\frac{\sqrt{3}}{2} x$

$\Rightarrow \frac{\Delta y}{y}=\frac{\sqrt{3} x}{2 y} d x=\frac{2}{x} \times \frac{k x}{100}$

$\Rightarrow \frac{\Delta y}{y} \times 100=2 k$

Hence, the error in the area of the triangle is $2 k \%$.