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Solution for While Measuring the Side of an Equilateral Triangle an Error of K % is Made, the Percentage Error in Its Area is (A) K % (B) 2k % (C) K 2 % (D) 3k % - CBSE (Science) 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
(a) k %
(b) 2k %
(c) \[\frac{k}{2}\%\]

(d) 3k %

Solution

(b) 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?

APPEARS IN

 RD Sharma Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (with solutions)
Chapter 14: Differentials, Errors and Approximations
Q: 5 | Page no. 13

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Solution for question: While Measuring the Side of an Equilateral Triangle an Error of K % is Made, the Percentage Error in Its Area is (A) K % (B) 2k % (C) K 2 % (D) 3k % concept: Approximations. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
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