In `Delta PQR`, If `angleR=angleP, QR=4 cm and PR = 5 cm. Then, the length of PQ is

Options

A. 4 cm
B. 5 cm
C. 2 cm
D. 2.5 cm

Explanation

To solve the problem, we will use the properties of triangles, specifically the property that states that in a triangle, sides opposite to equal angles are equal.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- In triangle PQR, we are given that angle R = angle P.
- The length of side QR = 4 cm.
- The length of side PR = 5 cm.

2. **Use the Property of Triangles**:
- Since angle R = angle P, we can apply the property that states that the sides opposite equal angles are equal.
- This means that the side opposite angle R (which is PQ) is equal to the side opposite angle P (which is QR).

3. **Set Up the Equation**:
- Therefore, we have PQ = QR.

4. **Substitute the Known Length**:
- We know that QR = 4 cm, so we can substitute this value into our equation:
\[ PQ = 4 \text{ cm} \]

5. **Conclusion**:
- Thus, the length of PQ is 4 cm.

### Final Answer:
The length of PQ is 4 cm.

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