The measured length and breadth of a rectangle are written as (5.7 `+-` 0.1) cm and (3.4 `+-` 0.2) cm respectively. Calculate the area of the rectangle with error limits.

Explanation

Given `l` = 5.7 cm and `Deltal 0.1 `cm , b = 3.4 cm and `Delta` b = 0.2 cm. The area of the rectangle without error limit is,
A = `lxxb = (5.7 xx3.4) "cm"^(2) = 19.38 "cm"^(2) ~~ 19.4 "cm"^(2)`
Next the fractional error in A is
`(DeltaA)/(A)=(Deltal)/(l)+(Deltab)/(b)=(0.1)/(5.7)+(0.2)/(3.4)~~(0.02+0.06)=0.8`
`:." " DeltaA=0.8xxA~~0.08xx19.4"cm"^(2)~~1.6 "cm"^(2)`
Hence the area of the rectangle with error limit is `(19.4 pm 1.6 ) "cm"^(2)`