Given a square, its side was increased by 3 times m and the area of the square

Given a square, its side was increased by 3 times m and the area of the square increased by 128 cm2. What was the side of the square at the very beginning.

Let’s say that the starting side of the square was x cm.

In this case, its initial area was: x * x = x ^ 2

After the side of the square was enlarged 3 times, it was: 3 * x.

The new area of the square became equal to: 3 * x * 3 * x = 9 * x ^ 2 + 128.

The difference between the two areas was:

9 * x ^ 2 – x ^ 2 = 128.

8 * x ^ 2 = 128.

x ^ 2 = 128/8 = 16.

x = √16 = 4 cm (starting length of the side of the square).

So the new side length was:

3 * 4 = 12 cm.

Answer: The initial length of the square was 4 cm.