Question

The side of a square is 7 m with a possible error of 0.05 m. Use differentials to approximate the maximum relative error in calculating the area of the square. Remember that the area of a square with side length s is A

Answer 1

Explanation:

Given :

Length of the side of a square = 7 m

Possible error = 0.05 m

Area of the square of side s is
`$A=s^2$`

Therefore,
`$(dA)/(ds) = 2s$`

or dA = 2s . ds

dA = 2 x 7 x 0.05

= 0.7

Therefore, the percentage error is given by :

`$=(dA)/(A)* 100$`

`$=(0.7)/(49)* 100$`

= 1.4 %