Question

Find the perimeter of a square with side a. Are the perimeter of the square and the length of its side directly proportional quantities? a=2 cm

i need the quantities and Perimeter is
cm

Answer 1

The perimeter is 8 cm.

Yes, the perimeter of a square is directly proportional to its side length.

Explanation:

Given:

The side length of the square is,
`a=2\ cm`

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`

Plug in
`a=2\ cm` and find perimeter, 'P'. This gives,

`P=4* 2=8\ cm`

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`

Dividing both sides by 'a', we get:

`(P)/(a)=(4a)/(a)\\(P)/(a)=4(Constant)`

Therefore, the ratio of perimeter and side length is a constant. Hence, these are directly proportional quantities.