Can we drawn a triangle, ABC with AB=3 cm, BC= 3.5 cm and Ca=65 cm ?

Options

A. Yes
B. No
C. Can't be determined
D. None of these

Answer

To determine whether we can draw triangle ABC with the given side lengths AB = 3 cm, BC = 3.5 cm, and CA = 65 cm, 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.

### Step-by-Step Solution:

1. **Identify the sides of the triangle:**
- Let AB = 3 cm
- Let BC = 3.5 cm
- Let CA = 65 cm

2. **Apply the triangle inequality theorem:**
We need to check the following conditions:
- Condition 1: AB + BC > CA
- Condition 2: AB + CA > BC
- Condition 3: BC + CA > AB

3. **Check Condition 1:**
- Calculate AB + BC:
\[ AB + BC = 3 + 3.5 = 6.5 \text{ cm} \]
- Compare with CA:
\[ 6.5 \text{ cm} > 65 \text{ cm} \quad \text{(False)} \]

4. **Check Condition 2:**
- Calculate AB + CA:
\[ AB + CA = 3 + 65 = 68 \text{ cm} \]
- Compare with BC:
\[ 68 \text{ cm} > 3.5 \text{ cm} \quad \text{(True)} \]

5. **Check Condition 3:**
- Calculate BC + CA:
\[ BC + CA = 3.5 + 65 = 68.5 \text{ cm} \]
- Compare with AB:
\[ 68.5 \text{ cm} > 3 \text{ cm} \quad \text{(True)} \]

6. **Conclusion:**
Since Condition 1 is not satisfied (6.5 cm is not greater than 65 cm), we conclude that it is not possible to draw triangle ABC with the given side lengths.

### Final Answer:
No, we cannot draw triangle ABC with the given side lengths of AB = 3 cm, BC = 3.5 cm, and CA = 65 cm.