#### 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) 2*k* %

(c) \[\frac{k}{2}\%\]

(d) 3*k* %

#### Solution

(b) 2*k*%

Let x be the side of the triangle and *y *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?

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.