The side of an equilateral triangle is 5 unit | vedclass

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(A) Let $A$ be the area and $x$ be the side of an equilateral triangle. The formula for the area is $A = \frac{\sqrt{3}}{4} x^2$. Differentiating with

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$2$

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(A) Let $A$ be the area and $x$ be the side of an equilateral triangle. The formula for the area is $A = \frac{\sqrt{3}}{4} x^2$. Differentiating with respect to $x$, we get $\frac{dA}{dx} = \frac{\sqrt{3}}{4} (2x) = \frac{\sqrt{3}}{2} x$. The approximate change in area $\Delta A$ is given by $\Delta A \approx \frac{dA}{dx} \cdot \Delta x = \frac{\sqrt{3}}{2} x \cdot \Delta x$. The percentage error in area is given by $\frac{\Delta A}{A} 	imes 100$. Substituting the values: $\frac{\Delta A}{A} 	imes 100 = \frac{(\frac{\sqrt{3}}{2} x \cdot \Delta x)}{(\frac{\sqrt{3}}{4} x^2)} 	imes 100 = \frac{2 \Delta x}{x} 	imes 100$. Given $x = 5$ and $\Delta x = 0.05$, the percentage error is $\frac{2 	imes 0.05}{5} 	imes 100 = \frac{0.1}{5} 	imes 100 = 0.02 	imes 100 = 2\%$. Thus, the percentage error is $2$.

The side of an equilateral triangle is $5$ units. In measuring the side, an error of $0.05$ units is made. Then the percentage error in measuring the area of the triangle is

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