A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find :
BC, if B'C' = 15 cm. 

Answer

To solve the problem, we need to find the length of side BC of triangle ABC given that the triangle is enlarged about point O with a scale factor of 3, and the length of the corresponding side B'C' in the enlarged triangle is 15 cm.

### Step-by-Step Solution:

1. **Understand the Scale Factor**:
The scale factor of enlargement is given as 3. This means that every side length of the original triangle ABC is multiplied by 3 to get the corresponding side length in the enlarged triangle B'C'.

2. **Identify the Corresponding Sides**:
We know that B'C' corresponds to BC in triangle ABC. According to the problem, B'C' = 15 cm.

3. **Set Up the Relationship**:
Since the scale factor is 3, we can express the relationship between the sides of the triangles as:
\[ B'C' = 3 \times BC \]

4. **Substitute the Known Value**:
We know that B'C' = 15 cm. Therefore, we can substitute this value into the equation:
\[ 15 = 3 \times BC \]

5. **Solve for BC**:
To find BC, we need to isolate it in the equation. We can do this by dividing both sides by 3:
\[ BC = \frac{15}{3} \]
\[ BC = 5 \text{ cm} \]

6. **Conclusion**:
The length of side BC in triangle ABC is 5 cm.

### Final Answer:
BC = 5 cm

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