If the side of the square is increased by 4 cm, then its area will increase by 32 cm ^ 2. What is the side of the square?

1. Let us denote the length of a side of a square by X. Then its area is S = X ^ 2.

2. If the side of the square is increased by 4 cm, then its area is S2 = (X + 4) ^ 2.

3. We obtain the equation of the problem: S2 – S1 = (X + 4) ^ 2 – X ^ 2 = 32.

4. Let’s simplify the equation. We get: 8 * X + 16 = 32.

5. Hence X = 2 cm.

Answer: the side of the square is 2 cm.