Which of the following possibilities will form a triangle? A: Side = 15 cm, side = 7 cm, side = 7 cm B: Side = 15 cm, side = 7 cm, side = 9 cm C: Side = 14 cm, side = 6 cm, side = 7 cm D: Side = 14 cm, side = 6 cm, side = 8 cm
The Correct Answer and Explanation is:
Correct Answer: C and D
To determine which sets of side lengths can form a triangle, we use the triangle inequality theorem. This theorem states that for any three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let’s test each option:
A: 15 cm, 7 cm, 7 cm
- 15 + 7 = 22 > 7 ✔
- 15 + 7 = 22 > 7 ✔
- 7 + 7 = 14 < 15 ✘
Since one pair fails the triangle inequality, this cannot form a triangle.
B: 15 cm, 7 cm, 9 cm
- 15 + 7 = 22 > 9 ✔
- 15 + 9 = 24 > 7 ✔
- 7 + 9 = 16 > 15 ✔
All conditions are satisfied, so at first glance, this seems correct. However, we must re-express and double-check.
Actually: - 7 + 9 = 16
- 16 is just greater than 15
So it does form a triangle.
Correction: B is valid
C: 14 cm, 6 cm, 7 cm
- 14 + 6 = 20 > 7 ✔
- 14 + 7 = 21 > 6 ✔
- 6 + 7 = 13 < 14 ✘
One condition fails, so C is invalid
D: 14 cm, 6 cm, 8 cm
- 14 + 6 = 20 > 8 ✔
- 14 + 8 = 22 > 6 ✔
- 6 + 8 = 14 ✔ (equal but not less)
All conditions are either greater or equal but not failing. Hence, D is valid
Final Conclusion: The sets that can form a triangle are B and D.
Now let’s explain the concept:
A triangle is a closed figure with three sides. For any three segments to form a triangle, their lengths must satisfy the triangle inequality rule. The key idea is that no single side should be as long as or longer than the sum of the other two. If that happens, the figure will not close to form a triangle. This ensures that the sides can physically connect in space to form a triangle. In our case, only options B and D met all the necessary conditions.
