Which of the following is the set of measure of the sides of a triangle?

Options

A. 8 cm, 4 cm, 20 cm
B. 9 cm, 17 cm, 25 cm
C. 11cm, 16 cm, 28 cm
D. None of these

Answer

To determine which set of measures can form a triangle, we will use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's analyze each option step by step:

### Step 1: Analyze Part A - 8 cm, 4 cm, and 20 cm
1. **Check the first combination:**
- Sum of 8 cm and 4 cm = 8 + 4 = 12 cm
- Compare with the third side (20 cm): 12 cm < 20 cm (not valid)

2. **Check the second combination:**
- Sum of 8 cm and 20 cm = 8 + 20 = 28 cm
- Compare with the third side (4 cm): 28 cm > 4 cm (valid)

3. **Check the third combination:**
- Sum of 4 cm and 20 cm = 4 + 20 = 24 cm
- Compare with the third side (8 cm): 24 cm > 8 cm (valid)

However, since one combination fails (12 cm < 20 cm), this set does not form a triangle.

### Step 2: Analyze Part B - 9 cm, 17 cm, and 25 cm
1. **Check the first combination:**
- Sum of 9 cm and 17 cm = 9 + 17 = 26 cm
- Compare with the third side (25 cm): 26 cm > 25 cm (valid)

2. **Check the second combination:**
- Sum of 17 cm and 25 cm = 17 + 25 = 42 cm
- Compare with the third side (9 cm): 42 cm > 9 cm (valid)

3. **Check the third combination:**
- Sum of 9 cm and 25 cm = 9 + 25 = 34 cm
- Compare with the third side (17 cm): 34 cm > 17 cm (valid)

Since all combinations are valid, this set can form a triangle.

### Step 3: Analyze Part C - 11 cm, 16 cm, and 28 cm
1. **Check the first combination:**
- Sum of 11 cm and 16 cm = 11 + 16 = 27 cm
- Compare with the third side (28 cm): 27 cm < 28 cm (not valid)

Since the first combination fails, this set does not form a triangle.

### Step 4: Analyze Part D - None of these
Since we have found that only Part B can form a triangle, we do not need to analyze this option further.

### Conclusion
The only set of measures that can form a triangle is from Part B: 9 cm, 17 cm, and 25 cm.