The length and breadth of a rectangle are (5. | vedclass

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(C) Given: Length $l = (5.7 \pm 0.1) 	ext{ cm}$ and Breadth $b = (3.4 \pm 0.2) 	ext{ cm}$.The area $A$ is given by $A = l 	imes b = 5.7 	imes 3.4

Vedclass · Accepted Answer

$(19.38 \pm 1.48) 	ext{ cm}^2$

Vedclass · Answer

(C) Given: Length $l = (5.7 \pm 0.1) 	ext{ cm}$ and Breadth $b = (3.4 \pm 0.2) 	ext{ cm}$.The area $A$ is given by $A = l 	imes b = 5.7 	imes 3.4 = 19.38 	ext{ cm}^2$.The relative error in area is given by $\frac{\Delta A}{A} = \frac{\Delta l}{l} + \frac{\Delta b}{b}$.Substituting the values: $\frac{\Delta A}{A} = \frac{0.1}{5.7} + \frac{0.2}{3.4} = \frac{0.34 + 1.14}{19.38} = \frac{1.48}{19.38}$.Therefore,the absolute error $\Delta A = \left( \frac{1.48}{19.38} ight) 	imes A = \left( \frac{1.48}{19.38} ight) 	imes 19.38 = 1.48 	ext{ cm}^2$.Rounding to appropriate significant figures,$\Delta A \approx 1.5 	ext{ cm}^2$ and $A \approx 19.4 	ext{ cm}^2$.Thus,the area is $(19.4 \pm 1.5) 	ext{ cm}^2$. Note: Based on the provided options,$(19.38 \pm 1.48) 	ext{ cm}^2$ is the intended answer.

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

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