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The question states that triangle VWX is dilated by a scale factor of \( \frac{2}{3} \) to form triangle \( V'W'X' \). The task is to find the measure of side \( WX \).

We know:

1. Side \( W'X' \) of the new triangle is 12.
2. The scale factor is \( \frac{2}{3} \).

### Relationship:
The length of a side in the original triangle (\( WX \)) relates to the corresponding side in the dilated triangle (\( W'X' \)) as follows:
\[
W'X' = \text{Scale Factor} \times WX
\]

Rearranging for \( WX \):
\[
WX = \frac{W'X'}{\text{Scale Factor}}
\]

### Substitution:
\[
WX = \frac{12}{\frac{2}{3}}
\]

Dividing by a fraction is the same as multiplying by its reciprocal:
\[
WX = 12 \times \frac{3}{2} = 18
\]

### Final Answer:
The length of side \( WX \) is **18 units**.

Would you like further details or clarification on the dilation process?

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Here are some related questions for practice:
1. What is the length of \( VW \) in the original triangle?
2. How do you find the scale factor if \( WX \) and \( W'X' \) are given?
3. What happens to the area of the triangle during dilation with a scale factor?
4. Can you calculate the perimeter of the original triangle from this information?
5. How does the scale factor affect angles in the triangles?

**Tip:** Always remember that dilation affects side lengths but preserves angles!

A triangle VWX is dilated by a scale factor of 2/3 to form triangle V'W'X'. What is the measure of side WX?

Learn how to find the original length of a side in a triangle dilated by a scale factor of 2/3. Includes step-by-step calculations using dilation concepts, scale factor properties, and similar triangles. Perfect for Grades 8-10.

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