If ABC and ADE is the triangle where AB=4.5 cm, BC= 6 cm, DF=10 cm, BC is parallel to DF. Calculate the length of AC by using scale factor

To calculate the length of \(AC\) using the **scale factor**, let’s proceed systematically.

### Step 1: Identify corresponding triangles  
Given:
- \( \triangle ABC \) and \( \triangle ADE \)  
- \( BC \parallel DF \), which means that the triangles are **similar** (since corresponding angles are equal).  
- This similarity implies that the **sides are proportional**.

### Step 2: Set up the proportion  
The corresponding sides are:
- \( AB \) corresponds to \( AD \)  
- \( BC \) corresponds to \( DF \)  
- \( AC \) corresponds to \( AE \)

The **scale factor** between the two triangles will be the ratio of corresponding sides:
\[
\text{Scale Factor} = \frac{BC}{DF} = \frac{6}{10} = 0.6
\]

### Step 3: Apply the scale factor to find \( AC \)  
Since the triangles are similar, the ratio of any two corresponding sides must be equal to the scale factor.  
So, we can write the relation between \( AC \) and \( AE \) as:
\[
\frac{AC}{AE} = \frac{BC}{DF} = 0.6
\]

Now, let's express \( AE \) in terms of \( AC \). Since \( AE \) is longer than \( AC \), it will be:
\[
AE = AC \times \frac{DF}{BC} = AC \times \frac{10}{6}
\]

However, you haven’t provided the exact measurement of either \( AC \) or \( AE \). If you need to calculate only **\(AC\)** or verify another unknown, please provide the missing detail, or I can help you further with another approach. 

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Would you like me to explore further possibilities? For example, are you also interested in solving for \(AD\)? 

Here are **five related questions** you may ask next:
1. How do we use the Pythagorean theorem for similar triangles?
2. What are the criteria for two triangles to be similar?
3. If BC = 6 cm and DF = 12 cm, what would be the new length of AC?
4. How do scale factors affect area and perimeter?
5. How can proportionality help in real-life applications?

**Tip:** Always ensure the sides you compare are truly corresponding sides when working with similar triangles!

If ABC and ADE is the triangle where AB=4.5 cm, BC= 6 cm, DF=10 cm, BC is parallel to DF. Calculate the length of AC by using scale factor.

Learn how to calculate the length of AC in triangle ABC using the scale factor and the proportionality of similar triangles. Given AB=4.5 cm, BC=6 cm, and DF=10 cm, this solution explores key geometric principles and applies the triangle similarity theorem. Suitable for Grades 8-10.

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