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

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, $a=2\ cm$

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,

$P=4\times 2=8\ cm$

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:

$\frac{P}{a}=\frac{4a}{a}\\\frac{P}{a}=4(Constant)$

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