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

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

Answers (1)

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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