Question

What happens to the area of a square when its side is doubled$?$

Answer 1

Step 1: Finding the area of the square when the side is given

Let us consider a square with a side $\text{x cm}$

We know that area of square $={\left(\text{side}\right)}^2$

So, the area of the square with sides $\text{x cm}$$={\left(x\text{cm}\right)}^2$

$={\text{x}}^2{\text{cm}}^2$

Step 2: Finding the area of the square when the side is doubled

Let us consider a square with a side $\text{2x cm}$

So, the area of the square with sides $\text{2x cm}$$={\left(2x\text{cm}\right)}^2$

$=4{\text{x}}^2{\text{cm}}^2$

Step 3: Comparing both the areas

On comparing ${\text{x}}^2{\text{cm}}^2$ and ${\text{4x}}^2{\text{cm}}^2$, we get that ${\text{4x}}^2{\text{cm}}^2$ is four times ${\text{x}}^2{\text{cm}}^2$

So, when the side of the square is doubled, the area will become four times the initial one.

Hence, the area of the square becomes quadruple when its side is doubled.