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

Answer:

Step-by-step 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, $\frac{dA}{ds} = 2s$

or dA = 2s . ds

    dA = 2 x 7 x 0.05

          = 0.7

Therefore, the percentage error is given by :

$=\frac{dA}{A}\times 100$

$=\frac{0.7}{49}\times 100$

= 1.4 %