The triangles below are similar. By what ratio was triangle XYZ enlarged by to create triangle LMN? Use this information to calculate the length of the missing side. Show your work.

Answer:

Ratio: 3:2

LN = 18

Step-by-step explanation:

"similar" means that all the angles are the same and the sides were all increased by the same proportion.

Thus, we know that MN/YZ = LM/XY = NL/ZX

First, we need to find the ratio. To do this, we write MN/YZ as a fraction, and simplify.

MN/YZ = 15/10 = 3/2

(If you want, you can double check this using LM nd XY. 8 * 3/2 = 12, so this is correct)

To find the missing side, we simply multiply XZ by 3/2.

12 * 3/2 = 18, so LN = 18.

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