https://file.aiquickdraw.com/mathbot/file/1727366032432l6hlnlir.jpg

The image shows two pentagons, Pentagon G and Pentagon H, where Pentagon H is a scaled copy of Pentagon G. We are tasked with two things:

1. **Identifying the scale factor** between Pentagon G and Pentagon H.
2. **Finding the missing side length** of Pentagon G, represented as "X."

### Step 1: Identify the Scale Factor
To find the scale factor, we can compare corresponding sides from Pentagon G and Pentagon H. For instance, consider the sides:

- One pair: \( \frac{28 \text{ (Pentagon H)}}{35 \text{ (Pentagon G)}} \)
  
  \[
  \frac{28}{35} = \frac{4}{5} = 0.8
  \]

So, the scale factor is **0.8**.

### Step 2: Find the Missing Side Length
Now that we know the scale factor, we can find the missing side length "X" by comparing it to the corresponding side on Pentagon H. The corresponding side length in Pentagon H is 16.

We use the formula:
\[
X \times \text{scale factor} = \text{corresponding side in Pentagon H}
\]
\[
X \times 0.8 = 16
\]

Solving for \(X\):
\[
X = \frac{16}{0.8} = 20
\]

### Answers:
1. **Scale factor:** 0.8
2. **Missing side length (X):** 20

Would you like more details or explanations on any part?

Here are five related questions:
1. How do you calculate the scale factor when given two similar shapes?
2. What happens if the scale factor is greater than 1?
3. Can the scale factor be a negative number? Why or why not?
4. How do you find the area of two similar shapes when you know the scale factor?
5. How does the scale factor affect the perimeter of similar shapes?

**Tip:** Always check that the corresponding sides are used when finding the scale factor, as mismatches can lead to incorrect results.

Pentagon H is a scaled copy of Pentagon G. The side lengths for Pentagon G are 35, 50, and an unknown value X. The side lengths for Pentagon H are 28, 40, and 16. Identify the scale factor and find the missing side length X.

Learn how to calculate the scale factor between two similar pentagons and find the missing side length using proportions. This problem involves key geometry concepts suitable for Grades 7-9.

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