Question

finding the dimensions of a rectangle

josephine has a rectangular garden with an area of \\(2x^2 + x - 6\\) square feet.

which expressions can represent the length and width of the garden?

• length = \\(x^2 - 3\\) feet; width = \\(2\\) feet
• length = \\(2x + 3\\) feet; width = \\(x - 2\\) feet
• length = \\(2x + 2\\) feet; width = \\(x - 3\\) feet
• length = \\(2x - 3\\) feet; width = \\(x + 2\\) feet

Explanation:

Identify the area formula of a rectangle

$$ \text{Area} = \text{length} \times \text{width} = 2x^2 + x - 6 $$

Factor the quadratic expression

$$ 2x^2 + x - 6 = (2x - 3)(x + 2) $$

Match factors with the options

$$
LATEXBLOCK0
$$

Answer:

• length = \(x^2 - 3\) feet; width = 2 feet
• length = \(2x + 3\) feet; width = \(x - 2\) feet
• length = \(2x + 2\) feet; width = \(x - 3\) feet
• length = \(2x - 3\) feet; width = \(x + 2\) feet (Correct answer)