The construction of a `DeltaPQR` in which QR = 7 cm and `angleQ = 50^(@)` is NOT possible when (PQ – PR) is equal to____

Options

A. 4cm
B. 6cm
C. 9cm
D. 3cm

Answer

To determine the value of \( PQ - PR \) for which the construction of triangle \( PQR \) is not possible, we will use the triangle inequality theorem. This theorem states that for any triangle, the difference of the lengths of any two sides must be less than the length of the third side.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- \( QR = 7 \) cm
- \( \angle Q = 50^\circ \)

2. **Apply the Triangle Inequality Theorem**:
- According to the triangle inequality theorem, for triangle \( PQR \):
- \( PQ - PR < QR \)
- \( PR - PQ < QR \)
- \( PQ + PR > QR \)

3. **Focus on the Relevant Inequality**:
- We are specifically interested in the first inequality:
\[ PQ - PR < QR \]
- Substituting the value of \( QR \):
\[ PQ - PR < 7 \text{ cm} \]

4. **Determine the Condition for Non-Construction**:
- For the construction to be impossible, we need to find when the difference \( PQ - PR \) is equal to or greater than \( QR \):
\[ PQ - PR \geq 7 \text{ cm} \]

5. **Conclusion**:
- Therefore, the construction of triangle \( PQR \) is not possible when:
\[ PQ - PR = 7 \text{ cm} \]

### Final Answer:
The construction of triangle \( PQR \) is not possible when \( PQ - PR \) is equal to **7 cm**.

---