Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.
Make a contextual triangle-existence decision
Problem
Roads of lengths \(4~\text{mi}\), \(7~\text{mi}\), and \(12~\text{mi}\) are proposed as the sides of a triangular route. Can they form a nondegenerate triangle?
A contextual route still has to pass the same strict closure test as any triangle. We’ll sort the proposed lengths, compare the longest with the combined shorter lengths, measure any surplus or shortfall, and translate that decisive comparison back into whether the roads can actually close.
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