Question

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

• A. $k\%$
• B. $2k\%$
• C. $\frac{k}{2}\%$
• D. $3k\%$

Answer 1

Answer: (B)

$2k\%$

Area of equilateral triangle $A=\frac{\sqrt{3}}{4}{x}^2$

$\frac{dA}{dx}=\frac{\sqrt{3}}{2}x$

Given, percentage error in measuring side $=k\%$

$\Rightarrow \frac{\Delta x}{x}=\frac{k}{100}$

$\Rightarrow \Delta x=\frac{kx}{100}$

Now, approximate error in measuring A$=dA=\left(\frac{dA}{dx}\right)\Delta x$

$=\frac{k}{100}\frac{\sqrt{3}}{2}{x}^2=2k\%$ of A

Percentage error in measuring $A=2k\%$