Question

The length and breadth of a rectangle are (5.7 $\pm$ 0.1) cm and (3.4 $\pm$ 0.2) cm. Calculate area of the rectangle with error limits.

• A. (19.0 1.5).
• B. (19.4 1.5).
• C. (19.38 1.48).
• D. none of these

Answer 1

The correct option is A

(19.0 1.5).

Here, I = (5.7 $\pm$ 0.1)cm b = (3.4 $\pm$ 0.2)cm

Area A = I $\times$ b = 5.7 $\times$ 3.4 = 19.38 $c{m}^2$ = 19.0 $c{m}^2$ (rounding off to two significant figures)

$\therefore \frac{△A}{A}=\pm (\frac{△l}{l}+\frac{△b}{b})=\pm (\frac{0.1}{5.7}+\frac{0.2}{3.4})=\pm \left(\frac{0.34+1.14}{5.7\times 3.4}\right)$

$\frac{△A}{A}=\pm \frac{1.48}{19.38}\Rightarrow △A=\pm \frac{1.48}{19.38}\times A=\pm \frac{1.48}{19.38}\times 19.38=\pm 1.48$

$△A=\pm 1.5$ (rounding off to two significant figures); Area = (19.0 $\pm$ 1.5)sq.cm.