A triangle has a perimeter 13. The two shorter side, have integer lengths equal to x and x + 1. Which of the following could be the length of the other side.
- A) 2
- B) 6
- C) 8
- D) None
Show answer
Answer: B) 6
Explanation
B) 6. Let the third, longest side be y. Then 2x + 1 + y = 13, so y = 12 − 2x. The two shorter sides must add to more than y: 2x + 1 > 12 − 2x, so x ≥ 3. For y to be the longest, 12 − 2x ≥ x + 1, so x ≤ 3. Hence x = 3 and the sides are 3, 4 and 6.
Asked in: BAPEX 2017
Topic: Geometry and Mensuration