Question

The measurement of a side of a square is found to be 12 centimeters. Estimate the maximum allowable percent error in measuring the side if the error in computing the area cannot exceed 2.5%.

Answer 1

 If x= side of the square, and A = area of square, then  

A = x^2 

dA/dx = 2x, or 

dA = 2x*dx, where dx is the differential in x (same as error) 


dA/A = 2x*dx/(x^2) = 2*dx/x = 2*(0.05cm)/(15cm) = 0.00667 = 0.667% 

for b): 

if dA/A = 0.025 = 2*dx/x, then 

dx/x=(0.025)/2 = 0.0125 = 1.25 % 

 I hope I helped. :)