In a triangle PQR, PQ = 20 cm and PR = 6 cm, the side QR is :

Options

A. equal to 14 cm
B. less than 14 cm
C. greater than 14 cm
D. none of these

Answer

To find the length of side QR in triangle PQR, we can use the triangle inequality theorem. The 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, and 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 sides of the triangle**:
- Given:
- PQ = 20 cm
- PR = 6 cm
- We need to find QR.

2. **Apply the triangle inequality theorem**:
- According to the theorem, we have the following inequalities:
1. PQ + PR > QR
2. PQ + QR > PR
3. PR + QR > PQ

3. **Substituting the known values**:
- From the first inequality:
- 20 cm + 6 cm > QR
- 26 cm > QR
- Thus, QR < 26 cm

- From the second inequality:
- 20 cm + QR > 6 cm
- QR > 6 cm - 20 cm
- QR > -14 cm (This inequality is always true since lengths cannot be negative)

- From the third inequality:
- 6 cm + QR > 20 cm
- QR > 20 cm - 6 cm
- QR > 14 cm

4. **Combine the results**:
- From the inequalities we derived:
- 14 cm < QR < 26 cm

5. **Conclusion**:
- The length of side QR must be greater than 14 cm and less than 26 cm. Therefore, QR can take any value in the range (14 cm, 26 cm).