Question

An error of $2\%$ in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

• A. $2\%$
• B. $2.02\%$
• C. $4\%$
• D. $4.04\%$

Answer 1

The correct option is D $4.04\%$

Let the correct side of the square be $x$ cm.
Then, incorrect side $=x+\frac{2}{100}x=1.02x$
Correct area $=x^2$
Incorrect area $=(1.02x{)}^2=1.0404x^2$
$\therefore \%$ Error $=\left(\begin{array}{c}\frac{1.0404x^2-x^2}{x^2}\times 100\end{array}\right)\%$
$=(0.0404\times 100)\%$

$=4.04\%$