The constrution of `Delta`ABC , given that BC = 6cm, `angleB=45^(@)` is not possible when difference of AB and AC is equal to

Options

A. `6.9` cm
B. `5.2` cm
C. `5.0`cm
D. `4.0` cm

Explanation

To determine when the construction of triangle ABC is not possible, given that BC = 6 cm and angle B = 45 degrees, we need to analyze the conditions under which a triangle can be formed.

### Step-by-Step Solution:

1. **Understand the Triangle Inequality Theorem**:
The triangle inequality 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. This can be expressed as:
- AB + AC > BC
- AB + BC > AC
- AC + BC > AB

2. **Set Up the Known Values**:
From the problem, we know:
- BC = 6 cm
- Angle B = 45 degrees

3. **Define the Sides**:
Let:
- AB = x cm
- AC = y cm

4. **Apply the Triangle Inequality**:
For the triangle ABC to exist, we must satisfy the triangle inequalities. Specifically, we need:
- AB + AC > BC
- This translates to:
- x + y > 6

5. **Consider the Difference Condition**:
The problem states that the construction is not possible when the difference between AB and AC is equal to a certain value. We need to express this condition mathematically:
- |AB - AC| = |x - y| > BC
- This means:
- x - y > 6 or y - x > 6

6. **Combine the Conditions**:
From the above conditions, we can derive:
- If x - y > 6, then x > y + 6
- If y - x > 6, then y > x + 6

7. **Analyze the Implications**:
If either condition is true, it implies that the sum of the lengths of AB and AC cannot satisfy the triangle inequality:
- For example, if x > y + 6, then substituting into the inequality x + y > 6 leads to contradictions.

8. **Conclusion**:
Therefore, the construction of triangle ABC is not possible when the difference between AB and AC is greater than 6 cm.

### Final Answer:
The construction of triangle ABC is not possible when the difference of AB and AC is greater than 6 cm.