In a `DeltaABC`, D, E and F are the midpoints of BC, CA and AB respectively. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm respectively, the perimeter of `DeltaDEF` is a cm. The value of a/2 is

Answer

To solve the problem step by step, we will follow the given information about triangle ABC and its midpoints D, E, and F.

### Step-by-Step Solution:

1. **Identify the Triangle and Midpoints**:
- We have triangle ABC with sides AB = 7 cm, BC = 8 cm, and CA = 9 cm.
- D, E, and F are the midpoints of sides BC, CA, and AB respectively.

2. **Use the Midpoint Theorem**:
- According to the midpoint theorem, the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
- Therefore:
- EF (connecting midpoints E and F) = 1/2 * BC = 1/2 * 8 cm = 4 cm
- DE (connecting midpoints D and E) = 1/2 * AB = 1/2 * 7 cm = 3.5 cm
- DF (connecting midpoints D and F) = 1/2 * CA = 1/2 * 9 cm = 4.5 cm

3. **Calculate the Perimeter of Triangle DEF**:
- The perimeter of triangle DEF is the sum of the lengths of its sides:
\[ \text{Perimeter of } DEF = EF + DE + DF \]
- Substituting the values we calculated:
\[ \text{Perimeter of } DEF = 4 \text{ cm} + 3.5 \text{ cm} + 4.5 \text{ cm} = 12 \text{ cm} \]

4. **Assign the Perimeter to A**:
- We are given that the perimeter of triangle DEF is A cm. Therefore, we have:
\[ A = 12 \text{ cm} \]

5. **Calculate A/2**:
- Finally, we need to find the value of A/2:
\[ \frac{A}{2} = \frac{12}{2} = 6 \text{ cm} \]

### Final Answer:
The value of \( \frac{A}{2} \) is **6 cm**.