Question

While measuring the side of a square an error of 7% in excess is made what is percentage error in area of square?

Answer 1

Answer:

A = L^2     area of square

A + dA = (L + .07 L)^2       where dA is error in A due to error in  L

A + dA = L^2 * (1 + .07)^2  = L^2 * ( 1 + .14 + .0049) = 1.14 = L^2 + 2  *L *dL

(the term .0049 is usually omitted because it is small)

A + dA - A = L^2 + 2 L dL -  L^2      

or dA = 2 L dL = .14 L      where dA and dL  are the errors involved

dA / A = 2 L dL / L^2 = 2 dl / L = 2 * 7% = 14 %       where dL / L is fractional error in L