Question

8. A rectangle is measured to be 6.4 +0.2 cm by 8.3 $0.2 cm.

a) Calculate its perimeter in cm

b) Calculate the uncertainty in its perimeter.

Answer 1

a) The perimeter of the rectangle is 29.4 centimeters.

b) The uncertainty in its perimeter is 0.8 centimeters.

Step-by-step explanation:

a) From Geometry we remember that the perimeter of the rectangle (
`p`), measured in centimeters, is represented by the following formula:

`p = 2\cdot (w+l)` (1)

Where:

`w` - Width, measured in centimeters.

`l` - Length, measured in centimeters.

If we know that
`w = 6.4\,cm` and
`l = 8.3\,cm`, then the perimeter of the rectangle is:

`p = 2\cdot (6.4\,cm+8.3\,cm)`

`p = 29.4\,cm`

The perimeter of the rectangle is 29.4 centimeters.

b) The uncertainty of the perimeter (
`\Delta p`), measured in centimeters, is estimated by differences. That is:

`\Delta p = 2\cdot (\Delta w + \Delta l)` (2)

Where:

`\Delta w` - Uncertainty in width, measured in centimeters.

`\Delta l` - Uncertainty in length, measured in centimeters.

If we know that
`\Delta w = 0.2\,cm` and
`\Delta l = 0.2\,cm`, then the uncertainty in perimeter is:

`\Delta p = 2\cdot (0.2\,cm+0.2\,cm)`

`\Delta p = 0.8\,cm`

The uncertainty in its perimeter is 0.8 centimeters.