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, ![a=2\ cm](https://tex.z-dn.net/?f=a%3D2%5C%20cm)
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:
![P=a+a+a+a=4a](https://tex.z-dn.net/?f=P%3Da%2Ba%2Ba%2Ba%3D4a)
Plug in
and find perimeter, 'P'. This gives,
![P=4\times 2=8\ cm](https://tex.z-dn.net/?f=P%3D4%5Ctimes%202%3D8%5C%20cm)
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, ![P=4a](https://tex.z-dn.net/?f=P%3D4a)
Dividing both sides by 'a', we get:
![\frac{P}{a}=\frac{4a}{a}\\\frac{P}{a}=4(Constant)](https://tex.z-dn.net/?f=%5Cfrac%7BP%7D%7Ba%7D%3D%5Cfrac%7B4a%7D%7Ba%7D%5C%5C%5Cfrac%7BP%7D%7Ba%7D%3D4%28Constant%29)
Therefore, the ratio of perimeter and side length is a constant. Hence, these are directly proportional quantities.