Sam decides to build a square garden. If the area of the garden is 9x2 − 24x + 16 square feet, what is the length of one side of the garden? (3x + 4) feet (3x − 4) feet (4x − 3) feet (4x + 3) feet

To find the length of one side of the square garden, we need to determine the side length from the given area expression, which is $9x^2 - 24x + 16$ square feet.

Step 1: Recognize that the area of a square is given by the square of its side length. Therefore, we need to express $9x^2 - 24x + 16$ as a perfect square trinomial.

Step 2: Factor the quadratic expression $9x^2 - 24x + 16$.

Step 3: Check if the quadratic expression can be written in the form $(ax + b)^2$.

Let's factor $9x^2 - 24x + 16$:

$9x^2 - 24x + 16 = (3x - 4)^2$

Step 4: Verify the factorization by expanding $(3x - 4)^2$:

$(3x - 4)^2 = (3x - 4)(3x - 4) = 9x^2 - 12x - 12x + 16 = 9x^2 - 24x + 16$

The factorization is correct.

Step 5: Identify the side length of the square garden. Since the area is $(3x - 4)^2$, the length of one side of the garden is $3x - 4$ feet.

Therefore, the correct answer is:

$(3x - 4)$ feet