https://file.aiquickdraw.com/mathbot/file/1729256117269kfts4xik.jpg

The problem involves two similar rectangles (denoted as "likformiga" in Swedish), meaning their corresponding sides are proportional. We're tasked with finding the length of the side marked with \( x \) in the smaller rectangle.

The dimensions are:
- Small rectangle: height = 2, width = \( x \)
- Large rectangle: height = 9, width = 3

Since the rectangles are similar, the ratio of the corresponding sides must be equal. This gives us the following proportion:

\[
\frac{x}{3} = \frac{2}{9}
\]

Now we solve for \( x \):

\[
x = \frac{2}{9} \times 3 = \frac{6}{9} = \frac{2}{3}
\]

So, the length of the side marked with \( x \) is \( \frac{2}{3} \).

Would you like more details or have any further questions? Here are 5 follow-up questions you might consider:

1. What does it mean for two shapes to be "similar" in geometry?
2. How can we verify that the proportion method works for similar figures?
3. Can the proportion method be used for all polygons, or is it specific to rectangles?
4. What would change if the large rectangle’s height was doubled?
5. How would you handle this problem if one of the dimensions was missing?

**Tip:** When working with similar figures, always check if corresponding sides are proportional before applying a solution.

Rektanglarna är likformiga. Hur lång är sidan markerad med x?

Learn how to solve for the missing side of a smaller rectangle using proportions and similar figures. This geometry problem involves understanding how to set up a proportion between corresponding sides of two similar rectangles. Suitable for Grades 6-8.

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