Question

When an error of 1% is made in the length and breadth of a rectangle, the percentage error (%) in the area of a rectangle will be options: a)0

b.1

c.2

d.4?

Answer 1

2%
Area = length * breadth
dA/A = dl/l + db/b
= 1+1 = 2%

Answer 2

Given,

Error in length and breadth = 1%

To Find,

Error in the area of a rectangle =?

Solution,

Error in length = (ΔL / L)*100 = 1%

Error in breadth = (ΔB / B)*100 = 1%

Error in the area of rectangle = (ΔA / A)*100 =  (ΔL / L)*100 +  (ΔB / B)*100

(ΔA / A)*100 = (ΔL / L)*100 +  (ΔB / B)*100

(ΔA / A)*100 = 1% + 1%

(ΔA / A)*100 = 2%

Error in the area of rectangle = 2%

Hence, when an error of 1% is made in the length and breadth of a rectangle, the percentage error (%) in the area of a rectangle will be 2%. Option(c) is the correct answer.