A triangle ABC has been enlarged by scale factor m = 2.5 to the triangle A' B'C' Calculate :
the length of C'A' if CA = 4 cm. 

Answer

To find the length of C'A' after the triangle ABC has been enlarged by a scale factor of m = 2.5, follow these steps:

### Step-by-Step Solution:

1. **Identify the given information**:
- The scale factor \( m = 2.5 \)
- The length of side CA = 4 cm

2. **Understand the relationship between the original triangle and the enlarged triangle**:
- When a triangle is enlarged by a scale factor, each side of the triangle is multiplied by that scale factor.
- Therefore, if the original length of side CA is denoted as \( b \), the length of the corresponding side in the enlarged triangle (C'A') will be \( m \times b \).

3. **Substitute the known values**:
- Here, \( b = CA = 4 \) cm.
- Thus, the length of C'A' can be calculated as:
\[ C'A' = m \times CA = 2.5 \times 4 \]

4. **Calculate the length**:
- Performing the multiplication:
\[ C'A' = 2.5 \times 4 = 10 \text{ cm} \]

5. **State the final answer**:
- Therefore, the length of C'A' is 10 cm.

### Final Answer:
C'A' = 10 cm