In `Delta PQR, PQ = 4cm, PR = 6 cm and QR =3 cm`. Which of the following is correct?

Options

A. `angle Q = angle R`
B. `angle R lt angle P`
C. `angle R gt angle Q`
D. `angle Q gt angle R`

Answer

To solve the problem regarding triangle PQR with sides PQ = 4 cm, PR = 6 cm, and QR = 3 cm, we will analyze the relationship between the angles based on the lengths of the sides.

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
- PQ = 4 cm
- PR = 6 cm
- QR = 3 cm

2. **Determine the longest and shortest sides**:
- The longest side is PR (6 cm).
- The shortest side is QR (3 cm).

3. **Apply the triangle inequality theorem**:
- In any triangle, the angle opposite the longest side is the largest angle, and the angle opposite the shortest side is the smallest angle.
- Therefore, angle Q (opposite side PR) is the largest angle, and angle P (opposite side QR) is the smallest angle.

4. **Rank the angles**:
- Since PR is the longest side, angle Q is the largest.
- Since QR is the shortest side, angle P is the smallest.
- Angle R, which is opposite side PQ (4 cm), will be in between angle Q and angle P.

5. **Establish the relationships**:
- We can conclude that:
- Angle Q > Angle R > Angle P

6. **Evaluate the options given**:
- Option 1: Angle Q = Angle R (False)
- Option 2: Angle R < Angle P (False)
- Option 3: Angle R > Angle Q (False)
- Option 4: Angle Q > Angle R (True)

### Conclusion:
The correct relationship is that angle Q is greater than angle R, which corresponds to option 4.