Final answer:
In a mathematical context, having a negative width as a solution when solving for the width of a rectangle is considered an extraneous solution because distances are non-negative in real life applications. The context of the problem and physical limits of actual objects validate this.
Step-by-step explanation:
When solving for the width of a rectangle, if the solution results in a negative width, this is considered an extraneous solution. The width of a rectangle is a measurement of distance and in real life settings, a negative distance doesn't exist. In the context of mathematics, negative values can be valid in certain situations like displacement or debt, but not in measurements of physical dimensions such as the width of a rectangle.
Furthermore, even if the equation provided two solutions due to an unknown squared term, in a physical context like this, only one positive value would be reasonable. For example, width values should fall within a realistic range based on the unit of measurement, such as the recorded measurement of width as 1.25 cm in the example given. It can't be less than 0 or larger than the actual object itself.
In conclusion, the width cannot be a negative number due to the context of the problem and the physical limits of actual objects, making the width equal to -10 an extraneous solution.
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