Question

In the given figure, there are three squares of sides 2 cm, 3 cm, and 4 cm. Their areas increase with an increase in their side length. Are they in direct proportion?

$$\begin{array}{cc}Side& Area\\ 2cm& \\ 3cm& \\ 4cm& \\ 5cm& \end{array}$$

Answer 1

Let's find the area of all three squares:
We know that the area of a square = side $\times$ side
For a square of 2 cm,
Area = 2 cm $\times$ 2 cm = 4 sq. cm

For a square of 3 cm,
Area = 3 cm $\times$ 3 cm = 9 sq. cm

For a square of 4 cm
Area = 4 cm $\times$ 4 cm = 16 sq. cm

For a square of 5 cm
Area = 5 cm $\times$ 5 cm = 25 sq. cm

$$\begin{array}{cc}Side& Area\\ 2cm& 4sq.cm\\ 3cm& 9sq.cm\\ 4cm& 16sq.cm\\ 5cm& 25sq.cm\end{array}$$

Here, as the side length of the square increases, the area of the square also increases, but the ratio of these two parameters is not constant.

Hence, the side length and the area of a square are not in direct proportion.