Final answer:
The area A = x² + 10x + 25 can be factored to (x + 5)², meaning the rectangle is a square with the dimensions for both length and width being x + 5.
Step-by-step explanation:
When given the area of a rectangle as a polynomial, A = x² + 10x + 25, it is implied that the length and width are factors of this polynomial. To find expressions for the dimensions, we can factor the polynomial. The quadratic A = x² + 10x + 25 can be factored as (x + 5)(x + 5) or (x + 5)², showing that both the length and width of the rectangle are x + 5. Dimensional analysis helps us remember the correct formulas for various geometric figures by using units. For example, the area of a square is always a product of two lengths, giving us dimension L².
In a geometric context, if we were given the side length of a square, we could find its area by squaring that length. Similarly, with the area of a rectangle being A = x² + 10x + 25, recognizing the perfect square trinomial allows us to identify that the rectangle is also a square with sides of length x + 5 in this case.