Question
The side of a square is 5 cm. If its side is doubled, how many times is the area of the new square bigger than the area of the old square?
Answers
GPT-4o mini
The area of a square is calculated using the formula:
\[
\text{Area} = \text{side}^2
\]
For the original square with a side length of 5 cm:
\[
\text{Area}_{\text{old}} = 5^2 = 25 \, \text{cm}^2
\]
If the side of the square is doubled, the new side length becomes:
\[
\text{side}_{\text{new}} = 2 \times 5 = 10 \, \text{cm}
\]
Now, we calculate the area of the new square:
\[
\text{Area}_{\text{new}} = 10^2 = 100 \, \text{cm}^2
\]
Next, we need to find how many times the area of the new square is bigger than the area of the old square:
\[
\text{Factor} = \frac{\text{Area}_{\text{new}}}{\text{Area}_{\text{old}}} = \frac{100}{25} = 4
\]
Thus, the area of the new square is **4 times** the area of the old square.
\[
\text{Area} = \text{side}^2
\]
For the original square with a side length of 5 cm:
\[
\text{Area}_{\text{old}} = 5^2 = 25 \, \text{cm}^2
\]
If the side of the square is doubled, the new side length becomes:
\[
\text{side}_{\text{new}} = 2 \times 5 = 10 \, \text{cm}
\]
Now, we calculate the area of the new square:
\[
\text{Area}_{\text{new}} = 10^2 = 100 \, \text{cm}^2
\]
Next, we need to find how many times the area of the new square is bigger than the area of the old square:
\[
\text{Factor} = \frac{\text{Area}_{\text{new}}}{\text{Area}_{\text{old}}} = \frac{100}{25} = 4
\]
Thus, the area of the new square is **4 times** the area of the old square.