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.

The measured length and breadth of a rectangle are written as (5.7 +-

1.	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.
Answer» SOLUTION :Given `l` = 5.7 cm and `Deltal 0.1 `cm , b = 3.4 cm and `Delta` b = 0.2cm. 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)`