Aworker is cutting a square from a piece of sheet metal. the specifications call for an area that is 16 cm squared with an error of no more than 0.03 cm squared. how much error could be tolerated in the length of each side to ensure that the area is within the tolerance?

Given:

area of square, A = 16

error in area, dA = 0.03 cm^{2}

Step-by-Step Explanation:

Let 'a' be the side of the square

area of square, A =                 (1)

A = 16 =  

Therefore, a = 4 cm

for max tolerable error in length 'da', differentiate eqn (1) w.r.t 'a':

dA = 2a da

da =

da = 0.0375 cm

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: