Question

which are the possible side lengths of a triangle?
○ 3 cm, 5 cm, 9 cm
○ 4 cm, 8 cm, 10 cm
○ 6 cm, 9 cm, 17 cm
○ 8 cm, 10 cm, 18 cm

Explanation:

To determine the possible side lengths of a triangle, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Step 1: Check 3 cm, 5 cm, 9 cm

• \(3 + 5 = 8\), and \(8 < 9\). So, this does not satisfy the triangle inequality theorem.

Step 2: Check 4 cm, 8 cm, 10 cm

• \(4 + 8 = 12\), and \(12 > 10\)
• \(4 + 10 = 14\), and \(14 > 8\)
• \(8 + 10 = 18\), and \(18 > 4\)

All three conditions are satisfied.

Step 3: Check 6 cm, 9 cm, 17 cm

• \(6 + 9 = 15\), and \(15 < 17\). So, this does not satisfy the triangle inequality theorem.

Step 4: Check 8 cm, 10 cm, 18 cm

• \(8 + 10 = 18\), and \(18 = 18\) (not greater than). So, this does not satisfy the triangle inequality theorem.

Answer:

B. 4 cm, 8 cm, 10 cm