In `Delta PQR, angle P = 75^(@), angle Q = 35^(@)` and `angle R = 70^(@)` then

Options

A. `PQ gt PR`
B. `PR gt QR`
C. `PQ lt PR`
D. None of these

Answer

To solve the problem, we need to determine the relationship between the lengths of the sides of triangle PQR based on the angles given.

### Step-by-Step Solution:

1. **Identify the Angles**:
- Angle P = 75°
- Angle Q = 35°
- Angle R = 70°

2. **Determine the Largest Angle**:
- Among the angles, 75° (Angle P) is the largest angle.

3. **Apply the Triangle Inequality Theorem**:
- The side opposite the largest angle is the longest side.
- Therefore, the side opposite Angle P (which is side QR) will be the longest side.

4. **Identify the Sides Opposite Each Angle**:
- Side QR is opposite Angle P (75°).
- Side PR is opposite Angle Q (35°).
- Side PQ is opposite Angle R (70°).

5. **Rank the Sides Based on the Angles**:
- Since QR is opposite the largest angle (75°), it is the longest side.
- The next largest angle is 70° (Angle R), which means side PQ is the second longest.
- The smallest angle is 35° (Angle Q), which means side PR is the shortest.

6. **Conclusion**:
- Based on the above reasoning, we can conclude that:
- QR > PQ > PR

### Final Answer:
- Therefore, the correct relationship is that QR is the longest side, followed by PQ, and PR is the shortest side.