A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find :
OA, if OA' = 6 cm. 

Answer

To solve the problem, we need to find the distance OA given that the distance OA' (the distance after enlargement) is 6 cm and the scale factor of enlargement is 3.

### Step-by-Step Solution:

1. **Understand the Scale Factor**: The scale factor of enlargement is given as 3. This means that every distance from the center of enlargement (point O) to any point on the triangle (like A) is multiplied by 3 to get the distance to the corresponding point in the enlarged triangle (A').

2. **Set Up the Relationship**: Let OA be the distance from point O to point A. According to the scale factor, the distance OA' (from O to A') will be:
\[ OA' = 3 \times OA \]

3. **Substitute the Given Value**: We know from the problem that:
\[ OA' = 6 \text{ cm} \]
Therefore, we can write:
\[ 3 \times OA = 6 \]

4. **Solve for OA**: To find OA, we can rearrange the equation:
\[ OA = \frac{6}{3} = 2 \text{ cm} \]

5. **Final Answer**: Thus, the distance OA is:
\[ OA = 2 \text{ cm} \]