Question

The length and breadth of a rectangle are $(5.5 \pm 0.1) cm$ and $(2.5 \pm 0.1) cm$. Calculate area of the rectangle with error limit.

• A. $(13 \pm 0.8) cm ^{2}$
• B. $(14 \pm 0.8) cm ^{2}$
• C. $(13 \pm 0.6) cm ^{2}$
• D. $(14 \pm 0.6) cm ^{2}$

Answer 1

Answer: (B)

$A =$ L.b. $=(5.5 \times 2.5)=13.75\, cm ^{2} \approx 14 \,cm ^{2}$
$\frac{\Delta A }{ A }=\frac{\Delta \ell}{\ell}+\frac{\Delta b }{ b }=\frac{0.1}{5.5}+\frac{0.1}{2.5}$
$\Delta A =(5.5 \times 2.5) \frac{(0.1)(2.5+5.5)}{(5.5 \times 2.5)}$
$ \Rightarrow 0.8 \,cm ^{2}$