D and F are the mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E.
Find AB, if `EF=4.8cm`.

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Draw the Triangle and Identify Points**:
- Start by drawing triangle ABC. Mark points D and F as the midpoints of sides AB and AC respectively.

2. **Draw the Parallel Line**:
- Draw a line through point F that is parallel to side AB. This line will intersect side BC at point E.

3. **Identify the Parallelogram**:
- Since DF is parallel to AB and EF is also parallel to AB, quadrilateral DEF is a parallelogram.

4. **Use Properties of the Parallelogram**:
- In a parallelogram, opposite sides are equal. Therefore, EF is equal to BD (EF = BD).

5. **Substitute the Given Value**:
- We know from the problem that EF = 4.8 cm. Hence, BD = 4.8 cm.

6. **Relate BD to AB**:
- Since D is the midpoint of AB, we can express BD as half of AB. Therefore, we can write BD = 1/2 * AB.

7. **Set Up the Equation**:
- Substitute the value of BD into the equation:
\[ 4.8 \text{ cm} = \frac{1}{2} \times AB \]

8. **Solve for AB**:
- To find AB, multiply both sides of the equation by 2:
\[ AB = 4.8 \text{ cm} \times 2 = 9.6 \text{ cm} \]

9. **Final Answer**:
- Therefore, the length of AB is 9.6 cm.