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

Here, $l=(5.7\pm 0.1)cm,b=(3.4\pm 0.2)cm$
Area, A = $l\times b=5.7\times 3.4=19.38c{m}^2=19.0c{m}^2$ (rounding off to two significant figures)
$\therefore \frac{△A}{A}=\pm (\frac{△l}{l}+\frac{△b}{b})$
= $\pm (\frac{0.1}{5.7}+\frac{0.2}{3.4})=\pm \left(\frac{0.34+1.14}{5.7\times 3.4}\right)=\pm \frac{1.48}{19.38}$
$\Rightarrow △A=\pm \frac{1.48}{19.38}\times A=\pm \frac{1.48}{19.38}\times 19.38=\pm 1.48$
$△A=\pm 1.5$ (rounding off to two significant figures);
Area = $(19.0\pm 1.5)c{m}^2$.