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The problem presents two triangles, one of which is a reduced version of the other. We are given some dimensions and need to find the longest side of the original triangle.

The triangles are similar, meaning the sides are proportional. The shortest side of the original triangle is 22 cm, and the shortest side of the reduced triangle is 8 cm. The longest side of the reduced triangle is 12 cm, and we need to find the longest side of the original triangle, denoted as \( x \).

The relationship between the triangles can be written as:

\[
\frac{22}{8} = \frac{x}{12}
\]

Now solve for \( x \):

\[
x = \frac{22}{8} \times 12 = \frac{22 \times 12}{8} = \frac{264}{8} = 33 \, \text{cm}
\]

So, the longest side of the original triangle is 33 cm.

Would you like more details on this solution or have any questions?

Here are 5 related questions to explore:

1. How do we know that the triangles are similar?
2. How would the solution change if the reduced triangle had different side lengths?
3. What is the ratio of the areas of the two triangles?
4. How do we use proportional reasoning in everyday situations?
5. Can we generalize this method to other shapes besides triangles?

**Tip:** In problems involving similar triangles, always look for proportional relationships between corresponding sides.

On the school copy machine, Mr. Douglas reduced a triangle so that it would fit better in student portfolios. The shortest side of the original triangle was 22 cm; other measurements are shown in the diagram. How long was the longest side of the original triangle?

Learn how to determine the longest side of an original triangle by using the properties of similar triangles and proportions. This problem is ideal for students in Grades 7-10, involving geometric similarity and proportional reasoning.

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