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 original square

For a square with area \(A^{2}\), using the formula \(A = s^{2}\) (where \(s\) is side - length), we get \(s=\sqrt{A^{2}}=A\).

Step2: Find side length of enlarged square

For a square with area \(25A^{2}\), using the formula \(A = s^{2}\), we get \(s=\sqrt{25A^{2}} = 5A\).

Step3: Determine the change in side - length

The original side - length is \(A\) and the new side - length is \(5A\). The ratio of the new side - length to the original side - length is \(\frac{5A}{A}=5\).

Answer:

The side length was multiplied by 5.