Question

the error in measurement of the sides of a rectangle is 1%. the error in the measurement of its area is .
(A) 1%
(B) 1/2%
(C) 2%
(D) None of the above...​

Answer 1

$\huge\rm\underline\purple{Answer:-}$

2%.

Explanation :

Since, we know the formulae of the area is known to be length*breadth. So, the the error in the length and breadth separately will be L*B or deltaL + deltaB where the value of the length and breadth error are 1% respectively.

So, the error in the area will be 1+1= 2%. Since, there are no multiple or power of the variables hence the error will be same.

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Answer 2

Answer: 2%

Explanation: Let sides of rectangle be L,B ;then area would be L×B

A=L×B,,taking log both sides we get lnA=lnL+lnB and differentiate both sides we will get ΔA/A=ΔL/L+ΔB/B. As RHS is equal to 2% as given in question so LHS is equal to 2% ,so our required answer is 2%