In a triangle the lengths of two sides are 5 and 9 and the length of the third side is represented by x. Which statement is always true?
Answer: D) 4 < x < 14
- A) x > 5
- B) x < 9
- C) 5 <= x <= 9
- D) 4 < x < 14
- E) None of these
Explanation
D) 4 < x < 14. In any triangle, each side is shorter than the sum of the other two and longer than their difference. So 9 − 5 < x < 9 + 5, which is 4 < x < 14. The other options are not always true: x could be 4.5, below 5, or 13, above 9.
Asked in: SGFL 2017
Topic: Geometry and Mensuration