Question

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 1

To find the ratio by which triangle XYZ was enlarged to create triangle LMN, compare the corresponding side lengths. Use this information to calculate the length of the missing side.

Step-by-step explanation:

To find the ratio by which triangle XYZ was enlarged to create triangle LMN, we can compare the corresponding side lengths. Let's say triangle XYZ has side lengths x, y, and z, and triangle LMN has side lengths a, b, and c. The ratio of side lengths is given by:


a/x = b/y = c/z

Now, let's use the information given to calculate the length of the missing side. We know that the scale length is 3 inches, and the unknown length is x. So, using the ratio:


a/3 inches = c/x inches

Solving for x, we get:


x = (3 inches * c) / a

Answer 2

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.