Check whether \(x=12\) is meaningful for rectangle area \(A=x(10-x)\) when \(\text{both}~\text{side}~\text{lengths}\) must be positive. Test \(x>0\) and \(10-x>0\) separately, compute the second side, and state the resulting contextual domain and conclusion.

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Yes. Since 12>0, the first positive-side constraint is enough.

No. Although 12>0, the other side is 10−12=−2, so x=12 is outside (0,10).

Yes. Since 12 is real, both modeled side lengths are valid.

Yes. Since |10−12|=2 is positive, the second side is valid.

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Curriculum context

Course: Math II
Standard: F-IF.5
Category: Functions
Domain: Interpreting Functions
Objective: Relate the domain of a quadratic function to its graph and situation.
Problem type: Decide whether a given input is meaningful for a quadratic model in context