An equilateral triangle has a side of 10 unit | vedclass

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Question

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

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$1$

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(C) Let $A$ be the area and $x$ be the side of an equilateral triangle. The area of an equilateral triangle is given by $A = \frac{\sqrt{3}}{4} x^2$. Differentiating both sides 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 the area is given by $\frac{\Delta A}{A} 	imes 100$. Substituting the values: $	ext{Percentage error} = \frac{\frac{\sqrt{3}}{2} x \Delta x}{\frac{\sqrt{3}}{4} x^2} 	imes 100 = \frac{2 \Delta x}{x} 	imes 100$. Given $x = 10$ and $\Delta x = 0.05$: $	ext{Percentage error} = \frac{2 	imes 0.05}{10} 	imes 100 = \frac{0.1}{10} 	imes 100 = 1 \%$. Thus, the percentage error in the area is $1 \%$.

An equilateral triangle has a side of $10$ units. If an error of $0.05$ units is made in measuring the side, then the percentage error in the area of the triangle is:

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