Questions: 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.)

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: 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: Identify Corresponding Sides

Since triangles $ \triangle ABC $ and $ \triangle XYZ $ are similar, their corresponding sides are proportional. Identify the corresponding sides:

$ AB $ corresponds to $ XY $
$ BC $ corresponds to $ YZ $
$ AC $ corresponds to $ XZ $

Step 2: Set Up Proportions

Given:

$ AB = 8 $
$ XY = 32 $
$ YZ = 64 $
$ BC = y $

Set up the proportion using the corresponding sides: \[ \frac{AB}{XY} = \frac{BC}{YZ} \]

Step 3: Substitute Known Values

Substitute the known values into the proportion: \[ \frac{8}{32} = \frac{y}{64} \]

Step 4: Solve for the Missing Side Length

Solve the proportion for $ y $: \[ \frac{8}{32} = \frac{y}{64} \] \[ \frac{1}{4} = \frac{y}{64} \] \[ y = \frac{64}{4} \] \[ y = 16 \]

Final Answer

The missing side length $ y $ is $ 16 $.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!