https://file.aiquickdraw.com/mathbot/file/1727194667544xv5r9ms2.jpg

In the image provided, we are given two quadrilaterals, \( G \) and \( H \), where quadrilateral \( H \) is a scaled copy of quadrilateral \( G \). The side lengths of quadrilateral \( G \) are 40, 40, 45, and some unknown side. In quadrilateral \( H \), the corresponding side lengths are 32, 32, and the unknown side labeled \( i \).

### To find the value of \( i \):

Since \( H \) is a scaled copy of \( G \), we can use the ratio of corresponding sides to find \( i \).

1. Compare the corresponding sides of \( G \) and \( H \). The two known sides in quadrilateral \( G \) are both 40, and the corresponding sides in \( H \) are both 32.
   
   \[
   \text{Scale factor} = \frac{32}{40} = \frac{4}{5}
   \]

2. Now, apply this scale factor to the unknown side \( 45 \) in quadrilateral \( G \) to find \( i \) in quadrilateral \( H \).

   \[
   i = \frac{4}{5} \times 45 = 36
   \]

Thus, the value of \( i \) is **36**.

Would you like further details or explanations? 

### Related Questions:
1. How do you determine the scale factor between two similar figures?
2. What is the relationship between corresponding sides of similar polygons?
3. How can you verify that two polygons are similar?
4. What are the properties of quadrilaterals that help in determining similarity?
5. How would the calculation change if one side of quadrilateral \( G \) was unknown?

### Tip:
Always ensure that corresponding sides of similar polygons are compared when determining scale factors or unknown lengths.

What is the value of i in the scaled quadrilateral problem, where quadrilateral H is a scaled copy of quadrilateral G, with side lengths 40, 40, 45 in G and corresponding sides 32, 32 in H?

Learn how to find the value of the unknown side 'i' in a scaled copy of quadrilateral H based on the given side lengths in quadrilateral G. This problem uses proportions and scale factors, suitable for Grade 7 students.

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