In `DeltaABC, AB=5cm, AC=7cm`. If AD is the angle bisector of `angleA` Then `BD:CD` is :

Options

A. `25:49`
B. `49:25`
C. `6:1`
D. `5:7`

Answer

To solve the problem, we will use the Angle Bisector Theorem. According to this theorem, if a point D lies on the side BC of triangle ABC and AD is the angle bisector of angle A, then the following relationship holds:

\[ \frac{BD}{CD} = \frac{AB}{AC} \]

### Step-by-Step Solution:

1. **Identify the given lengths:**
- AB = 5 cm
- AC = 7 cm

2. **Apply the Angle Bisector Theorem:**
- According to the theorem:
\[ \frac{BD}{CD} = \frac{AB}{AC} \]
- Substitute the known values:
\[ \frac{BD}{CD} = \frac{5}{7} \]

3. **Express the ratio:**
- This means that the ratio of BD to CD is:
\[ BD : CD = 5 : 7 \]

4. **Conclusion:**
- Therefore, the final answer is:
\[ BD : CD = 5 : 7 \]