We are given two similar triangles: △LMN and △ABC, where the angles are similar, meaning their corresponding sides are in proportion.
Known lengths:
- MN = 15 cm
- AB = 6 cm
- BC = 9 cm
We are asked to find:
- Length of LM
- Length of AB (given as 6 cm, perhaps a typo, so we'll confirm calculations)
Step 1: Identify corresponding sides
Since the triangles are similar by angles LMN and ABC, the corresponding vertices align as:
- L corresponds to A
- M corresponds to B
- N corresponds to C
Thus, sides correspond as:
- LM corresponds to AB
- MN corresponds to BC
- LN corresponds to AC
Step 2: Use the ratio of corresponding sides
The similarity ratio (scale factor) between △LMN and △ABC can be found by comparing corresponding sides:
MN / BC = 15 cm / 9 cm = 5/3
This means the side lengths in △LMN are scaled up by a factor of 5/3 compared to △ABC.
Step 3: Find LM
Because LM corresponds to AB, and ratio LM / AB = 5/3, then:
LM = (5/3) × AB = (5/3) × 6 cm = 10 cm
Step 4: Re-examine AB
Given AB is 6 cm, which matches the original data.
Therefore, no calculation is needed for AB, it is already provided.
Final answers:
- LM = 10 cm
- AB = 6 cm (given)