Final answer:
The unknown horizontal length of triangle NOP can be found using the concept of similarity. Since triangles LMN and NOP are similar, the ratio of their corresponding side lengths will be equal. The ratio of the vertical heights of the triangles is 2:4, and since the vertical height of triangle LMN is 2 units, the vertical height of triangle NOP is 4 units.
Step-by-step explanation:
The unknown horizontal length of triangle NOP can be found using the concept of similarity. Since triangles LMN and NOP are similar, the ratio of their corresponding side lengths will be equal. The ratio of the vertical heights of the triangles is 2:4, and since the vertical height of triangle LMN is 2 units, the vertical height of triangle NOP is 4 units.
Using the ratio of side lengths, we can set up the following proportion:
3/2 = x/4
Cross-multiplying and solving for x, we find that the unknown horizontal length of triangle NOP is 6 units.