Question

Fill in the blanks: -
The unit of measurement of perimeter is the same as that of _____.

Answer 1

Hint: First of all we need to understand the meaning of the term ‘perimeter’. Further, we will see the formulas of perimeter of certain important 2 – D shapes like: - circle, square and rectangle. To find the dimension of perimeter we will see the physical quantities used in the formula of perimeter and the units that are used to measure these physical quantities.

Complete step by step answer:
Here we have been asked to find the unit of the perimeter and relate it with the unit of the correct physical quantity. First we need to understand the meaning of the term ‘perimeter’.
Now, the term ‘perimeter’ is used for a closed figure. It is defined as the total length of the outer boundary of the figure. Let us see the formulas of some of the important 2 – D shapes like: - circle, square and rectangle one by one.
(1) Circle: - We know that the ratio of circumference to the diameter of a circle is a constant known as $\pi $, so we have mathematically,

$\Rightarrow \pi =\dfrac{C}{d}$
Here C is the circumference, d is the diameter. We know that the diameter is twice the radius (r), so we get,
\[\begin{align}
  & \Rightarrow \pi =\dfrac{C}{2r} \\
 & \Rightarrow C=2\pi r \\
\end{align}\]
Clearly the unit of radius is meter because it is length so the unit of circumference will also be meter as 2 and $\pi $ are constants so they have no unit.
(2) Square: - We know that all the sides of a square are equal so let us assume each side as ‘a’. Therefore the perimeter will be the sum of all the sides given as: -

$\Rightarrow $ Perimeter of square = a + a + a + a
$\Rightarrow $ Perimeter of square = 4a
Here, 4 is a constant so it will have no unit while ‘a’ is length measured in meters, so the unit of the perimeter of a square will be meter.
(3)Rectangle: - We know that the pair of opposite sides of a rectangle is equal so let us assume the length of the rectangle as ‘l’ and breadth as ‘b’. Therefore the perimeter will be the sum of all the sides given as: -

$\Rightarrow $ Perimeter of rectangle = 2l + 2b
$\Rightarrow $ Perimeter of rectangle = 2(l + b)
Here, 2 is a constant so it will have no unit while ‘l’ and ‘b’ are measured in meters because they are lengths in nature, so their sum will also be in meters. Therefore, the unit of the perimeter of a rectangle will be meter.
Hence, on reading the above notes we can conclude that the unit of measurement of perimeter is the same as that of length.

Note: Note that the topic ‘errors and dimensions’ are an important topic in science. Without the dimensions there is no any significance of a physical quantity. You must remember that dimensions of certain basic quantities like unit of area is square meter, unit of measurement of volume is cubic meter. Generally we remember the units of seven fundamental quantities and derive the units of other quantities using them.