Question

Which of the following possibilities will form a triangle?

A. Side 15 cm, Side 6 cm, Side 8 cm.
B. Side 15 cm, Side 6 cm, Side 9 cm.
C. Side 16 cm, Side 9 cm, Side 6 cm.
D. Side 16 cm, Side 9 cm, Side 8 cm.

Answer 1

To determine if a triangle can be formed, we apply the Triangle Inequality Theorem by checking if the sum of the lengths of any two sides is greater than the length of the third side. Options A, B, and C form triangles.

Step-by-step explanation:

To determine whether a triangle can be formed, we need to apply the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check each option:

• Option A: 15 + 6 = 21, which is greater than 8. This option forms a triangle.
• Option B: 15 + 6 = 21, which is greater than 9. This option forms a triangle.
• Option C: 16 + 9 = 25, which is greater than 6. This option forms a triangle.
• Option D: 16 + 9 = 25, which is equal to 8. This option does not form a triangle.

Therefore, options A, B, and C form triangles.