Can a triangle have three sides whose length are
3 cm, 4 cm, 7 cm ?

Answer

To determine if a triangle can be formed with sides of lengths 3 cm, 4 cm, and 7 cm, we will use the triangle inequality theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
- Let the sides be \( a = 3 \) cm, \( b = 4 \) cm, and \( c = 7 \) cm.

2. **Check the triangle inequality conditions**:
- We need to check three conditions:
1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

3. **Evaluate the first condition**:
- Calculate \( a + b \):
\[ 3 + 4 = 7 \]
- Now check if \( 7 > 7 \):
- This is **not true** (7 is not greater than 7).

4. **Evaluate the second condition**:
- Calculate \( a + c \):
\[ 3 + 7 = 10 \]
- Now check if \( 10 > 4 \):
- This is **true**.

5. **Evaluate the third condition**:
- Calculate \( b + c \):
\[ 4 + 7 = 11 \]
- Now check if \( 11 > 3 \):
- This is **true**.

6. **Conclusion**:
- Since the first condition \( a + b > c \) is not satisfied (7 is not greater than 7), we conclude that a triangle cannot be formed with sides of lengths 3 cm, 4 cm, and 7 cm.

### Final Answer:
No, a triangle cannot have sides of lengths 3 cm, 4 cm, and 7 cm.