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.


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