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

Answer

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

### Step-by-Step Solution:

1. **Understand the Scale Factor**: The scale factor indicates how much larger the new triangle (A'B'C') will be compared to the original triangle (ABC). A scale factor of 3 means that every dimension of the triangle is multiplied by 3.

2. **Identify Points**: Let O be the center of enlargement. The points A, B, and C are the vertices of the original triangle, while A', B', and C' are the vertices of the enlarged triangle.

3. **Apply the Scale Factor**: According to the properties of enlargement:
- The distance from the center of enlargement O to the new point A' is given by:
\[ OA' = \text{Scale Factor} \times OA = 3 \times OA \]
- Similarly, for point B:
\[ OB' = 3 \times OB \]

4. **Formulate the Ratio**: We need to find the ratio of the distances from point O to the new point B' and the original point B:
\[ \frac{OB'}{OB} = \frac{3 \times OB}{OB} \]

5. **Simplify the Ratio**: The OB in the numerator and denominator cancels out:
\[ \frac{OB'}{OB} = 3 \]

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

---