The side of a square is 5 cm. How many times will the new area become, if the side of the square is doubled?

The correct option is 4 times.

Let us break down the problem step-by-step to understand how changing the side length of a square affects its total area.

Step 1: Calculate the original area of the square

The formula for the area of a square is given by:

$\text{Area}={\text{side}}^2$

Given that the original side length of the square is 5 cm:

${\text{Area}}_{\text{original}}={\left(5\text{cm}\right)}^2=25{\text{cm}}^2$

Step 2: Calculate the new side length and new area

When the side length of the square is doubled, the new side length becomes:

$\text{New side}=2\times 5\text{cm}=10\text{cm}$

Now, calculate the new area using the new side length:

${\text{Area}}_{\text{new}}={\left(10\text{cm}\right)}^2=100{\text{cm}}^2$

Step 3: Compare the new area with the original area

To find out how many times the area increases, divide the new area by the original area:

$\text{Ratio of areas}=\frac{{\text{Area}}_{\text{new}}}{{\text{Area}}_{\text{original}}}=\frac{100{\text{cm}}^2}{25{\text{cm}}^2}=4$

General Rule:

In general, if the side of any square of side $s$ is doubled to $2s$, its new area becomes ${\left(2s\right)}^2=4s^2$, which is always 4 times the original area ($s^2$).

Therefore, the new area becomes 4 times the original area.