Final answer:
To determine the length of each side of the square when the area is (9x² - 12x + 4) square units, the expression must be factored to (3x - 2)², indicating that the side length is (3x - 2) units.
Step-by-step explanation:
The area of a square is given as (9x² - 12x + 4) square units. To find the length of each side, we must factor the quadratic expression completely.
We notice that this expression is a perfect square trinomial because it can be factored into (3x - 2)².
The factored form indicates that the side length of the square is (3x - 2) units.
Since the area of a square is equal to the side length squared, the original area expression (9x² - 12x + 4) is the square of the length of the sides of the square.