Question

The error in the measurement of the sides of rectangle is 1% the error in measurement of its area

Answer 1

Answer:

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Answer 2

Answer:

The error in the measurement of the area of the rectangle is $0.01(l+b)$.

where,

$l$ and $b$ are the length and breadth of the rectangle respectively.

Explanation:

Let the length and the breadth of the rectangle be $l$ and $b$ respectively and $\Delta l$ and $\Delta b$ be the errors in the measurement of length and the breadth respectively.

Given that, $\Delta l=\Delta b = 1\%=\dfrac1{100} = 0.01$

The area of the rectangle is given by

$A=lb$

The error associated with the area of the rectangle is given by

$A\pm \Delta A = (l\pm \Delta l)(b\pm \Delta b)= lb \pm l\Delta b\pm b\Delta l+\Delta l\Delta b\\\Delta A=l\Delta b\pm b\Delta l\ \ \ \ \because A=lb\\\Delta A= l(0.01)+b(0.01)=0.01(l+b)$

It is the error in the measurement of the area of the rectangle.