a square with an area of $a^{2}$ is enlarged to a square with an area of $25a^{2}$. how was the side of the…

Explanation:

Step1: Find side - length of smaller square

Let the side - length of the smaller square be $s_1$. Since the area of a square is $A = s^2$, and the area of the smaller square is $A^2$, then $s_1^2=A^2$, so $s_1 = A$.

Step2: Find side - length of larger square

Let the side - length of the larger square be $s_2$. Since the area of the larger square is $25A^2$, and $A = s^2$, then $s_2^2=25A^2$, so $s_2 = 5A$.

Step3: Determine the change in side - length

To find how the side - length has changed, we divide $s_2$ by $s_1$: $\frac{s_2}{s_1}=\frac{5A}{A}=5$. This means the side - length of the smaller square was multiplied by 5.

Answer:

The side length was multiplied by 5.