A student uses a metre scale, measuring upto $1\ mm$, to measure the length an breadth of a retangular plate. He finds that length$=5.7\ cm$ and breadth $=3.4\ cm$. What is the percentage error in the area of the plate?

$\begin{aligned} \text { Now } \rightarrow \text { Area } &=\text { Length } \times \text { Bredth. } \\ A &=l \times b=57 \times 34=1938 \mathrm{~mm}^{2} \end{aligned}$

$\begin{array}{l} \text { Using error analysis } \rightarrow \\ \text { Take logarithm both sides } \\ \qquad \log A=\log (l)+\log (b) \end{array}$

$\begin{array}{l} \text { difterentiate both sides - } \\ \frac{d A}{A}=\frac{d l}{l}+\frac{d b}{b} \quad \Rightarrow d A=A\left[\frac{d l}{l}+\frac{d b}{b}\right] \end{array}$

$\frac{d A}{A}=1938\left[\frac{1}{57}+\frac{1}{34}\right]=0.047=4.7 \%$