Final answer:
The side length of the square garden, given its area as a quadratic expression 9x² - 24x + 16, is found by factoring the expression into a binomial. The correct factored form is (3x - 4), so the length of one side of the garden is 3x - 4 feet.
Step-by-step explanation:
The question deals with finding the length of one side of a square garden given the area in the form of a quadratic expression. Factoring quadratic expressions is a useful skill in algebra that helps to solve various problems including geometric applications.
The area of the garden is given by 9x² - 24x + 16 square feet, which is a perfect square trinomial. To find the side length of the garden, we need to find a binomial (a two-term algebraic expression) that, when squared, gives us the trinomial.
Factoring the expression:
- Identify a perfect square that matches the first term, 9x², which is (3x)².
- Identify a perfect square that matches the last term, 16, which is 4².
- Since the middle term is negative, we'll look for two identical terms that multiply to 9x² and add up to -24x.
- These terms are -4x and -4x because (3x)(-4) = -12x, and doubled gives -24x.
- So the binomial that squares to the given trinomial is (3x - 4), and this will be the length of one side of the square garden.
Therefore, the correct answer is 2) 3x - 4 feet.