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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

#### 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.

$\frac{∆ x}{x} \times 100 = k$

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

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

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

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

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

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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 (A) K % (B) 2k % (C) K 2 % (D) 3k % Concept: Approximations.
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