Question

The measures of length and breadth of a rectangle are (30$\pm$3%) and (10$\pm$0.5%) metre. Calculate the percentage error in the perimeter.

• A. $2.4$%
• B. $3.5$%
• C. $1.9$%
• D. $4$%

Answer 1

The correct option is A $2.4$%

Here, length, $l=30m$ , % error in length $=\Delta l/l\times 100=3$ or $\Delta l=3l/100=3\left(30\right)/100=0.9$

and breadth, $b=10m$ , % error in breadth $=\Delta b/b\times 100=0.5$ or $\Delta b=0.5b/100=0.5\left(10\right)/100=0.05$

Perimeter , $p=2(l+b)$

So, $\frac{\Delta p}{p}=\frac{\Delta l+\Delta b}{l+b}$

Percetage error in perimeter, $\frac{\Delta p}{p}\times 100=\frac{0.9+0.05}{30+10}\times 100=2.4\%$