Length and breadth of a rectangle are (5.7 pm 0.1) cm and (3.4 pm 0.2) cm , respectively. Calculate

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The length and breadth of a rectangle are $(5.7 \pm 0.1) cm$ and $(3.4 \pm 0.2) cm$, respectively. Calculate the area of rectangle with error limits.

$(15.07 \pm 0.18) sq.cm$

$(17.07 \pm 0.98) sq.cm$

$(19.38 \pm 1.48) sq.cm$

$(16.07 \pm 1.18) sq.cm$

Solution

Here, $l=(5.7 \pm 0.1) cm , b =(3.4 \pm 0.2) cm$

Area, $A=l \times b=5.7 \times 3.4=19.38 cm ^{2}=19.0 cm ^{2}$

$\frac{\Delta A }{ A }=\pm\left(\frac{\Delta l }{ l }+\frac{\Delta b }{ b }\right)$$=\pm\left(\frac{0.1}{5.7}+\frac{0.2}{3.4}\right)=\pm\left(\frac{0.34+1.14}{5.7 \times 3.4}\right)$$=\pm \frac{1.48}{19.38}$

$\Rightarrow \triangle A =\pm \frac{1.48}{19.38} \times A =\pm \frac{1.48}{19.38} \times 19.38=\pm 1.48$

$\triangle A =\pm 1.5$

Area $=(19.0 \pm 1.5) cm ^{2}$

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