Final Answer:
The dimensions of the tabletop can be determined from the quadratic expression x² + 14x + 49. To find the dimensions, we need to factorize the quadratic equation. Factoring the quadratic expression x² + 14x + 49 gives us (x + 7)(x + 7), indicating that the tabletop has dimensions of length (x + 7) units and width (x + 7) units, or more succinctly, a square shape with each side measuring (x + 7) units.
Step-by-step explanation:
The given polynomial x² + 14x + 49 models the area of the tabletop. To determine the dimensions, we factorize the quadratic expression. Factoring x² + 14x + 49 results in (x + 7)(x + 7) since both terms in the expression are perfect squares. This factorization indicates that the tabletop's area expression can be represented as (x + 7)². Therefore, the tabletop's dimensions are expressed in terms of (x + 7) units for both the length and the width.
The factorization (x + 7)(x + 7) implies that the tabletop is square-shaped, as both factors are the same, indicating equal dimensions for the length and width. Each side of the tabletop measures (x + 7) units. Thus, the tabletop can be visualized as a square with side length (x + 7) units. This representation helps in understanding that the tabletop's dimensions are equal, forming a square with sides of length (x + 7) units.
The polynomial x² + 14x + 49, when factorized to (x + 7)(x + 7), signifies that the tabletop's area expression can be simplified to (x + 7)², where (x + 7) represents the length (or width) of the tabletop. Therefore, the dimensions of the tabletop are such that both the length and width are (x + 7) units, illustrating a square-shaped tabletop.