Two sides of a rectangle were measured. One of the sides (length) was measured 10% more than its actual length and the other side (width) was measured 5% less than its actual length. The percentage error in measure obtained for the area of the rectangle is :

Answer: Option A

Let the actual length and width of the rectangle be $$l$$ and b respectively.
Then, measured length :
$$=100\%\text{ of }l=\frac{11l}{10}$$
Measured width :
$$=95\%\text{ of }b=\frac{19b}{20}$$
Actual area = $$lb$$
Measured area :
$$\begin{array}{rl}& =\left(\frac{11l}{10}\times \frac{19b}{20}\right)\\ & =\frac{209lb}{200}\end{array}$$
Error in measurement :
$$\begin{array}{rl}& =\left(\frac{209lb}{200}-lb\right)\\ & =\frac{9lb}{200}\end{array}$$
∴ Error % :
$$\begin{array}{rl}& =\left(\frac{9lb}{200}\times \frac{1}{lb}\times 100\right)\%\\ & =4.5\%\end{array}$$