Question

A rectangle has a length of 2.3 plus or minus .2 m and a width of 1.2 plus or minus .2m. Calculate the area and the perimeter of the rectangle and give the uncertainty of each.

Answer 1

Given:

The length of the rectangle, l=2.3±0.2 m

The width of the rectangle, w=1.2±0.2 m

To find:

The area and the perimeter of the rectangle with the uncertainty in each value.

Step-by-step explanation:

The area of a rectangle is given by,

`A=l* w`

On substituting the known values,

`\begin{gathered} A=(2.3\pm0.2)*(1.2\pm0.2) \\ =(2.3*1.2)\pm((0.2)/(2.3)+(0.2)/(1.2)) \\ =2.8\pm0.3\text{ m}^2 \end{gathered}`

The perimeter of the rectangle is given by,

`P=2(l+w)`

On substituting the known values,

`\begin{gathered} P=2[(2.3\pm0.2)+(1.2\pm0.2)] \\ =2[(2.3+1.2)\pm(0.2+0.2)] \\ =2[3.5\pm0.4] \\ =(7.0\pm0.8)\text{ m} \end{gathered}`

Final answer:

The area of the rectangle is 2.8±0.3 m²

The perimeter of the rectangle is 7.0±0.8 m