Question

The sides of a rectangle are $(10.5\pm 0.2)$cm and $(5.2\pm 0.1)cm$. Calculate its perimeter with error limits.

Answer 1

Length $=(10.5\pm 0.2)$

Breadth $=(5.2\pm 0.1)$

$l=10.5$

$\delta l=0.2$

$b=5.2$

$\delta b=0.1$

perimeter $P=2(l+b)$

$=2(10.5+5.2)$

$=2\left(15.7\right)$

$=31.4cm$

Absolute error in perimeter $=\delta P=\pm 2(\delta l+\delta b)$

$=\pm 2(0.2+0.1)$

$=\pm 2\left(0.3\right)$

$=\pm 0.6cm$

Perimeter with error limits

$(P\pm \delta P)=(31.4\pm 0.6)cm$