Questions: Similarity Finding a missing side length given two similar triangles triangle ABC and triangle XYZ are similar. Find the missing side length. (The triangles are not drawn to scale.)

Similarity

Finding a missing side length given two similar triangles

triangle ABC and triangle XYZ are similar. Find the missing side length.
(The triangles are not drawn to scale.)

Transcript text: Similarity Finding a missing side length given two similar triangles $\triangle A B C$ and $\triangle X Y Z$ are similar. Find the missing side length. (The triangles are not drawn to scale.)

Solution

Solution Steps

Step 1: Find the scale factor.

The ratio of corresponding sides XZ and AC is 56/7 = 8. Therefore, the scale factor is 8.

Step 2: Set up a proportion.

Let the missing side be represented by _x_. The side _x_ of triangle ABC corresponds to the side XY of triangle XYZ. So, we can set up the proportion:

x / 32 = 7 / 56 = 8/ BC

Step 3: Solve for x.

Since the scale factor is 8 and XY = 32, we can write the equation:

x * 8 = 32

x = 32 / 8 = 4