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

Answer:

a) The perimeter of the rectangle is 29.4 centimeters.

b) The uncertainty in its perimeter is 0.8 centimeters.

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.