Question

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 smaller square changed?
the side length was increased by 5.
the side length was multiplied by 5.
the side length was increased by 10.
the side length was multiplied by 10.

Explanation:

Step1: Find side - length of smaller square

Let side of smaller square be $s_1$. Since area of square $A = s^2$, for area $A^2$, $s_1 = A$.

Step2: Find side - length of larger square

Let side of larger square be $s_2$. For area $25A^2$, $s_2=\sqrt{25A^2}=5A$.

Step3: Determine side - length change

$\frac{s_2}{s_1}=\frac{5A}{A}=5$, so side length was multiplied by 5.

Answer:

The side length was multiplied by 5.