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

Answer 1

Answer: (B)

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