Question

Question was provided via image upload.

Explanation:

Factor the area polynomial

Using the Factoring Polynomials knowledge point

$$
LATEXBLOCK0
$$

Determine the length of the rectangle

Using the Polynomial Division knowledge point

$$
LATEXBLOCK1
$$

Calculate the perimeter of the rectangle

Using the Polynomial Addition knowledge point

$$
LATEXBLOCK2
$$

Evaluate the given statements

• Statement 1: "The rectangle is a square." Since \(4x - 1

eq x + 10\), this is false.

• Statement 2: "The rectangle has a length of \((2x - 5)\) units." Since the length is \(4x - 1\), this is false.
• Statement 3: "The perimeter of the rectangle is \((10x + 18)\) units." This matches our calculated perimeter, so this is true.
• Statement 4: "The area of the rectangle can be represented by \((4x^2 + 20x - 2x - 10)\) square units." This simplifies to \(4x^2 + 18x - 10\), which is false.

Answer:

• The rectangle is a square.
• The rectangle has a length of \((2x - 5)\) units.
• The perimeter of the rectangle is \((10x + 18)\) units. (Correct answer)
• The area of the rectangle can be represented by \((4x^2 + 20x - 2x - 10)\) square units.