Final Answer:
The possible rectangle dimensions are (x - 5) and (x + 5).
Explanation:
To find the dimensions of the rectangle, we need to factorize the given expression, x³ - 25. This expression can be expressed as a difference of cubes, where x³ - 25 is equivalent to (x - 5)(x² + 5x + 25). The dimensions of the rectangle are determined by the factors, (x - 5) and (x² + 5x + 25). The factor (x - 5) represents one dimension, while (x² + 5x + 25) represents the other. Therefore, the possible rectangle dimensions are (x - 5) and (x + 5).
In the factorization process, we recognize the pattern of a difference of cubes, where a³ - b³ can be factored as (a - b)(a² + ab + b²). Here, x³ - 25 is treated as (x)³ - (5)³, leading to the factorization (x - 5)(x² + 5x + 25).
The dimension (x - 5) corresponds to one side of the rectangle, and the quadratic factor (x² + 5x + 25) relates to the other side. Consequently, the dimensions of the rectangle are (x - 5) and (x + 5), reflecting the factors obtained from the factorization of the given expression.