Final answer:
The area of the rectangle (x^2 - 9) can be factored into (x + 3)(x - 3) using the difference of squares method. These factored terms could represent the length and breadth of the rectangle, with care taken so that the dimensions do not turn out negative.
Step-by-step explanation:
The area of a rectangle is generally the product of its length and breadth. If the area of a rectangle is given by an expression like (x^2 - 9), this expression can be factored using the difference of squares method. The difference of squares formula is a^2 - b^2 = (a + b)(a - b).
In this case x^2 - 9 can be factored into (x + 3)(x - 3). So, one possible pair for the length and breadth of the rectangle could be x + 3 and x - 3.
It's important to remember that in the real world, the dimensions of a rectangle must be positive, and so the value of x used should ensure that none of these dimensions turn out negative.
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