Answer:
The perimeter is 8 cm.
Yes, the perimeter of a square is directly proportional to its side length.
Step-by-step explanation:
Given:
The side length of the square is, [tex]a=2\ cm[/tex]
The perimeter of a square is the sum of all of its side lengths. The perimeter of a square of side length 'a' is given as:
[tex]P=a+a+a+a=4a[/tex]
Plug in [tex]a=2\ cm[/tex] and find perimeter, 'P'. This gives,
[tex]P=4\times 2=8\ cm[/tex]
Therefore, the perimeter is 8 cm.
Now, two quantities are directly proportional only if their ratio is a constant.
Let us find the ratio of 'P' and 'a'.
We have, [tex]P=4a[/tex]
Dividing both sides by 'a', we get:
[tex]\frac{P}{a}=\frac{4a}{a}\\\frac{P}{a}=4(Constant)[/tex]
Therefore, the ratio of perimeter and side length is a constant. Hence, these are directly proportional quantities.
