A triangle ABC has been enlarged by scale factor m = 2.5 to the triangle A' B'C' Calculate :
the length of AB, if A' B' = 6 cm.

Answer

To solve the problem, we need to find the length of side AB in triangle ABC, given that triangle ABC has been enlarged to triangle A'B'C' by a scale factor of m = 2.5, and that the length of side A'B' is 6 cm.

### Step-by-Step Solution:

1. **Understand the Scale Factor**: The scale factor of enlargement is given as m = 2.5. This means that each side of triangle ABC is multiplied by 2.5 to get the corresponding side in triangle A'B'C'.

2. **Identify the Corresponding Sides**: Let’s denote the sides of triangle ABC as follows:
- Side AB = C
- Side BC = A
- Side CA = B

After enlargement, the corresponding sides in triangle A'B'C' will be:
- Side A'B' = 2.5 * C
- Side B'C' = 2.5 * A
- Side C'A' = 2.5 * B

3. **Set Up the Equation**: We know from the problem that:
\[ A'B' = 6 \text{ cm} \]
Since A'B' corresponds to side BC in triangle ABC, we can express this as:
\[ 2.5C = 6 \]

4. **Solve for C**: To find the length of side AB (which is C), we need to isolate C in the equation:
\[ C = \frac{6}{2.5} \]

5. **Calculate C**: Now, perform the division:
\[ C = \frac{6}{2.5} = 2.4 \text{ cm} \]

6. **Conclusion**: Therefore, the length of side AB is:
\[ AB = 2.4 \text{ cm} \]

### Final Answer:
The length of AB is 2.4 cm.

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