Question

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

Options

• k %

• 2k %

• \[\frac{k}{2}\%\]

• 3k %

Answer 1

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

\[\frac{∆ x}{x} \times 100 = k\]

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

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

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

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

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