Final answer:
The length of a side of the square defined by the area A(x) = x² - 12x + 36 is 'x - 6', which is option a.
Step-by-step explanation:
The area of a square is given by the function A(x) = x² - 12x + 36. The length of a side of the square can be found by taking the square root of the area. However, we recognize that the expression for the area is a perfect square trinomial, which factors into (x - 6)². Therefore, the length of a side of the square is x - 6, which corresponds to option a.
The area of a square is given by the formula A(x) = x² - 12x + 36. To find the length of a side of the square, we need to take the square root of the area. Therefore, the length of a side of the square is represented by the equation:
x - 6 (option a)