#### Please solve RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 5 maths textbook solution

Answer : B)  $2k%$

Hint:  Here, we know the formula of area of equilateral triangle,

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

Given:

Percentage error in measuring side$=k%$

Solution:

Area of equilateral triangle, $A=\frac{\sqrt{3}}{4} x^{2}$

Let’s differentiate,

$\frac{d A}{d x}=\frac{\sqrt{3}}{2} x$

Here, given percentage error in measuring side$=k%$

So,

\begin{aligned} &\frac{\Delta x}{x}=\frac{k}{100} \\\\ &\Delta x=\frac{k x}{100} \end{aligned}

Now, approximate error in measuring

\begin{aligned} A &=d A=\left(\frac{d A}{d x}\right) \Delta x \\\\ &=\frac{k}{100} \times \frac{\sqrt{3}}{2} x^{2} \end{aligned}

\begin{aligned} &=\frac{2 k}{100} \times \frac{\sqrt{3}}{4} x^{2} \\\\ &=2 k \% \text { of } A \end{aligned}

So, percentage error in measuring $A=2 k \%$

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