The mid points of AB and AC of the `DeltaABC` are P and Q respectively. If `PQ = 6 cm`, then the side BC is

Options

A. 10 cm.
B. 12 cm.
C. 8 cm.
D. 14 cm.

Answer

To solve the problem, we will use the properties of midpoints in a triangle. The midpoints of the sides of a triangle create a segment that is parallel to the third side and half its length.

### Step-by-Step Solution:

1. **Identify the Triangle and Midpoints**:
- We have triangle ABC with points P and Q as the midpoints of sides AB and AC, respectively.

2. **Understand the Relationship**:
- According to the midpoint theorem, the line segment connecting the midpoints of two sides of a triangle (PQ) is parallel to the third side (BC) and is half its length. This means:
\[ PQ = \frac{1}{2} \times BC \]

3. **Substitute the Given Value**:
- We know from the problem that \( PQ = 6 \, \text{cm} \). Therefore, we can substitute this value into the equation:
\[ 6 = \frac{1}{2} \times BC \]

4. **Solve for BC**:
- To find BC, we can multiply both sides of the equation by 2:
\[ BC = 2 \times 6 = 12 \, \text{cm} \]

5. **Conclusion**:
- Thus, the length of side BC is \( 12 \, \text{cm} \).

### Final Answer:
The length of side BC is **12 cm**.

---