In a `Delta ABC`, angle bisector of interior angle A meets BC at D . if AB = 25 cm & AC = 20 cm If length of CD = 16 cm find length of BC ?

Answer

To solve the problem, we will use the Angle Bisector Theorem, which states that the ratio of the lengths of the two segments created by the angle bisector on the opposite side is equal to the ratio of the lengths of the other two sides of the triangle.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Length of AB = 25 cm
- Length of AC = 20 cm
- Length of CD = 16 cm
- Let BD = x cm (we need to find this)

2. **Apply the Angle Bisector Theorem:**
According to the Angle Bisector Theorem:
\[ \frac{AB}{AC} = \frac{BD}{CD} \]
Substituting the known values:
\[ \frac{25}{20} = \frac{x}{16} \]

3. **Cross-Multiply to Solve for x:**
Cross-multiplying gives us:
\[ 25 \cdot 16 = 20 \cdot x \]
Simplifying this:
\[ 400 = 20x \]

4. **Solve for x:**
Divide both sides by 20:
\[ x = \frac{400}{20} = 20 \text{ cm} \]
Thus, BD = 20 cm.

5. **Find the Length of BC:**
Now, we can find the length of BC:
\[ BC = BD + CD = 20 \text{ cm} + 16 \text{ cm} = 36 \text{ cm} \]

### Final Answer:
The length of BC is **36 cm**.