Question

The Length And Breadth Of A Rectangle Are$(5.7\pm 0.1)cm$ And $(3.4\pm 0.2)cm$, respectively. Calculate The Area Of Rectangle With Error Limits.

Answer 1

As given:

Length -$L$= $(5.7\pm 0.1)cm$

Breadth $B$= $(3.4\pm 0.2)cm$

Area $A$= $L\times B$

$\Rightarrow 5.7\times 3.4$

$\Rightarrow 19.38c{m}^2$$=19.0c{m}^2$

Therefore, $\frac{∆A}{A}=\pm (\frac{∆L}{L}+\frac{∆B}{B})$

$\Rightarrow \pm (\frac{0.1}{5.7}+\frac{0.2}{3.4})$

$\Rightarrow \pm \frac{0.34+1.14}{5.7\times 3.4}$
$\Rightarrow \pm \frac{1.48}{19.38}$

$\Rightarrow ∆A=\pm (\frac{1.48}{19.38}\times 19.38)$

$\Rightarrow ∆A=\pm 1.48$

$\Rightarrow ∆A=\pm 1.5$ (By rounding off to two significant figures).

Area = $(19.0\pm 1.5)c{m}^2$