If two sides of a tringle are of length 5 cm and 1.5 cm, then the length of third side of the triangle cannot be

Options

A. 3.6 cm
B. 4.1 cm
C. 3.8 cm
D. 3.4 cm

Explanation

To determine the length of the third side of a triangle when two sides are given, we can use 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, and the difference between the lengths of any two sides must be less than the length of the third side.

Given:
- Side A = 5 cm
- Side B = 1.5 cm

Let’s denote the length of the third side as C.

### Step 1: Apply the Triangle Inequality Theorem

1. **Sum of the two sides must be greater than the third side:**
- A + B > C
- 5 cm + 1.5 cm > C
- 6.5 cm > C
- Therefore, C < 6.5 cm.

2. **Difference of the two sides must be less than the third side:**
- |A - B| < C
- |5 cm - 1.5 cm| < C
- 3.5 cm < C
- Therefore, C > 3.5 cm.

### Step 2: Determine the Range for C

From the inequalities we have derived:
- 3.5 cm < C < 6.5 cm

### Step 3: Identify Values that Cannot Be C

Now, we need to find the length of the third side that cannot be possible based on our derived range.

- Any value of C must be greater than 3.5 cm and less than 6.5 cm.
- Therefore, any value less than or equal to 3.5 cm is not possible.

### Conclusion

Thus, the length of the third side of the triangle cannot be 3.4 cm.

---