If the side of the square is increased by a meter. Its area will increase by 9 meters squared. What is the side of the square?

Suppose that the side of the square was equal to x meters, so its area was equal to S = x².
When the side of the square was increased by 1 meter, the side of the square was x + 1 meter, and the area became S = (x + 1) ².
Thus, according to the condition of the problem, we can compose the equation:
(x + 1) ² = x² + 9,
x² + 2 * x + 1 = x² + 9,
2 * x = 9 – 1,
x = 8: 2,
x = 4 (m) – the initial length of the side of the square.
Answer: 4 meters.