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. $(19.0\pm 5.5)$ sq.cm
• B. $(39.0\pm 1.5)$ sq.cm
  
• C. $(29.0\pm 2.5)$ sq.cm
  
• D. $(19.0\pm 1.5)$ sq.cm
  

Answer 1

Answer: (D)

$(19.0\pm 1.5)$ sq.cm

$l=(5.7\pm 0.1)cm$

$b=(3.4\pm 0.2)cm$

$A=l\times b$

$=5.7\times 3.4=19.38c{m}^2=19.0c{m}^2$

$\frac{\Delta A}{A}=\pm (\frac{\Delta l}{l}+\frac{\Delta b}{b})$

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

$=\pm \left(\frac{0.34+1.14}{5.7\times 3.4}\right)$

$\frac{\Delta A}{A}=\pm \frac{1.48}{19.38}$

$\Delta A=\pm \frac{1.48}{19.38}\times A$

$\Delta A=\pm \frac{1.48}{19.38}\times 19.38$

$\Delta A=\pm 1.48=\pm 1.5$

Therefore Area = $(19.0\pm 1.5)sq.cm$