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While Measuring the Side of an Equilateral Triangle an Error of K % is Made, the Percentage Error in Its Area is - CBSE (Commerce) Class 12 - Mathematics

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Question

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

  • k %

  • 2k %

  • \[\frac{k}{2}\%\]

  • 3k %

Solution

2k%
Let x be the side of the triangle and be its area.

\[\frac{∆ x}{x} \times 100 = k\]

\[\text { Also }, y = \frac{\sqrt{3}}{4} x^2 \]

\[ \Rightarrow \frac{dy}{dx} = \frac{\sqrt{3}}{2}x\]

\[ \Rightarrow \frac{∆ y}{y} = \frac{\sqrt{3}x}{2y}dx = \frac{2}{x} \times \frac{kx}{100}\]

\[ \Rightarrow \frac{∆ y}{y} \times 100 = 2k\]

\[\text { Hence, the error in the area of the triangle is } 2k  .\] %

  Is there an error in this question or solution?

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Solution While Measuring the Side of an Equilateral Triangle an Error of K % is Made, the Percentage Error in Its Area is Concept: Approximations.
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