Given that triangles LMN and ABC are similar, their corresponding sides are proportional.
Given:
- MN = 15 cm
- AB = 6 cm
- BC = 9 cm
The similarity means the corresponding sides are in proportion:
LM / AB = MN / BC
We can write this as:
LM / 6 = 15 / 9
Cross-multiplying:
LM = (15 / 9) × 6
Simplify the fraction 15 / 9:
15 / 9 = 5 / 3
Then,
LM = (5 / 3) × 6 = 5 × 2 = 10 cm
Answer: LM = 10 cm.