The length and breadth of a rectangular room are 15cmand 12cm respectively.if each of these measurements is liable to 1.5%error.calculate the absolute error inperimeter of the room

Question

Calculate the absolute error in the perimeter of the room

Answer 1

So the measurements can be off 1.5% in either direction, the answer is simply 3% because the formula for perimeter involves strict multiplication.

Here is the actual proof:

For measurement x, the actual measurement is x + 1.5% of x =

100% of x+ 1.5% of x =

101.5% of x =

1.015x

The other direction likewise can be found by doing 100% - 1.5% = 98.5% = 0.985

So essentially the real measurement is (1 +or- 0.015) * x where x is the measurement.

The length is measured as 15, so the real length is (1 +or- 0.015)*15

while the width (or breadth) is 12 ( 1 +or- 0.015)*12

Perimeter = 2 * length + 2 * width

= 2 * (1 +or- 0.015)*15 + 2 * 12 ( 1 +or- 0.015)*12

= ( 1 +or- 0.015) [ 2 * 15 + 2*12] <--- factors out the error

= ( 1 +or- 0.015) * actual perimeter

= old perimeter +or- 0.015 * actual perimeter

The absolute error is then 1.015 * actual perimeter - 0.985 * actual perimeter = 0.03 * actual perimeter

which is 3% of the actual perimeter