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Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches.
What is the greatest possible whole-number length of the unknown side?
2 inches
3 inches
7 inches
9 inches
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Answered by
GPT-5 mini
AI
For an obtuse triangle with longest side 14, we need 14^2 > 12^2 + x^2. So
196 > 144 + x^2 → x^2 < 52 → x < √52 ≈ 7.21.
Also triangle inequality gives x > 2. The greatest whole-number x less than 7.21 is 7.
Answer: 7 inches.
196 > 144 + x^2 → x^2 < 52 → x < √52 ≈ 7.21.
Also triangle inequality gives x > 2. The greatest whole-number x less than 7.21 is 7.
Answer: 7 inches.
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