A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find state the value of :
`(C’A’)/(CA)`

Answer

To solve the problem, we need to find the ratio \( \frac{C'A'}{CA} \) given that triangle ABC is enlarged about point O with a scale factor of 3.

### Step-by-Step Solution:

1. **Understanding the Scale Factor**:
The scale factor of enlargement is given as 3. This means that every length in the enlarged triangle (C'A'B') will be 3 times the corresponding length in the original triangle (ABC).

2. **Identifying the Corresponding Lengths**:
The sides of the triangles correspond to each other. Specifically, the length \( CA \) in triangle ABC corresponds to the length \( C'A' \) in triangle C'A'B'.

3. **Applying the Scale Factor**:
Since the scale factor is 3, we can express the relationship between the lengths:
\[ C'A' = 3 \times CA \]

4. **Finding the Ratio**:
Now we can find the ratio \( \frac{C'A'}{CA} \):
\[ \frac{C'A'}{CA} = \frac{3 \times CA}{CA} \]

5. **Simplifying the Ratio**:
When we simplify the ratio, we find:
\[ \frac{C'A'}{CA} = 3 \]

### Final Answer:
Thus, the value of \( \frac{C'A'}{CA} \) is \( 3 \).

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