The length and breadth of a rectangle room is 15cmand12cmrespectively if each of these measurement s is liable to 15% error calculate the error in the perimeter of the room

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

Explanation:

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