Geometry and TrigonometryVery hardTriangle inequality applied
Geometry and Trigonometry practice question
Which of the following could be the lengths of the three sides of a triangle?
- A. 4, 7, 10Correct
- B. 2, 3, 5
- C. 1, 4, 6
- D. 5, 5, 11
Answer: A. 4, 7, 10
Each pair of sides must sum to more than the third: 4 + 7 = 11 > 10 ✓ (and the other pairs clearly work).
Why the other answers are wrong
- B. 2, 3, 5
- 2 + 3 = 5, which equals the third side; the triangle would be flat.
- C. 1, 4, 6
- 1 + 4 = 5 < 6.
- D. 5, 5, 11
- 5 + 5 = 10 < 11.
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