Question

The length and breadth of rectangle are 5.7+-0.1 cm and 3.4+-0.2 cm .calculate area of rectangle with error limits.

Answer 1

Length = 5.7 ± 0.1 cm
breadth = 3.4 ± 0.2 cm

A = Lb
= (5.7 × 3.4)
= 19.38 cm²

ΔA = A × (ΔL/L + Δb/b)
= 19.38 × (0.1/5.7 + 0.2/3.4)
= 1.48 cm²

Area of rectangle = (19.38 ± 1.48) cm²

Answer 2

Answer:

The area of the rectangle with error limits is (19.38 ± 1.48) cm.

Given:

Dimensions of a rectangle,

Length,l= 5.7 ± 0.1 cm  

breadth,b = 3.4 ± 0.2 cm  

To find area of rectangle without the error limits,

We know that area of a square, A = l×b

On substituting the value,

A = (5.7 × 3.4)  

= 19.38 cm²

To find the area of rectangle with error limits,

ΔA = A × (ΔL/L  +Δb/b)  

= 19.38 × (0.1/5.7  +0.2/3.4)  

= 1.48 cm²

 

Finally the area of rectangle with the error limits = (19.38 ± 1.48) cm.