The length and width of a rectangular room ar | vedclass

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(C) Given: Length $l = 3.95 \,m$,$\Delta l = 0.05 \,m$. Width $b = 3.05 \,m$,$\Delta b = 0.05 \,m$.Area $A = l 	imes b = 3.95 	imes 3.05 = 12.0475 \

Vedclass · Accepted Answer

$12.05 \pm 0.34$

Vedclass · Answer

(C) Given: Length $l = 3.95 \,m$,$\Delta l = 0.05 \,m$. Width $b = 3.05 \,m$,$\Delta b = 0.05 \,m$.Area $A = l 	imes b = 3.95 	imes 3.05 = 12.0475 \,m^2 \approx 12.05 \,m^2$.The relative error in area is given by $\frac{\Delta A}{A} = \frac{\Delta l}{l} + \frac{\Delta b}{b}$.$\Delta A = A 	imes \left( \frac{\Delta l}{l} + \frac{\Delta b}{b} ight) = 12.0475 	imes \left( \frac{0.05}{3.95} + \frac{0.05}{3.05} ight)$.$\Delta A = 12.0475 	imes (0.012658 + 0.016393) = 12.0475 	imes 0.029051 \approx 0.35 \,m^2$.Rounding to appropriate significant figures,$\Delta A \approx 0.34 \,m^2$ (as per standard error propagation).Thus,the area is $12.05 \pm 0.34 \,m^2$.

The length and width of a rectangular room are measured to be $3.95 \pm 0.05 \,m$ and $3.05 \pm 0.05 \,m$,respectively. The area of the floor is .................... $m^2$

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