https://file.aiquickdraw.com/mathbot/file/17291702456542l4o6j52.jpg

In the given problem, Triangle 2 is a scale drawing of Triangle 1, meaning the two triangles are similar. Similar triangles have proportional sides. Let's use this information to find the length of side \(x\) in Triangle 2.

### Information from the image:
- **Triangle 1**:
  - Short leg = 12 cm
  - Long leg = 16 cm
  - Hypotenuse = 20 cm

- **Triangle 2**:
  - Short leg = 30 cm
  - Long leg = \(x\)
  - Hypotenuse = 50 cm

Since the triangles are similar, the ratio of corresponding sides is constant. The ratio between the hypotenuses is:

\[
\frac{50}{20} = \frac{5}{2}
\]

So, the sides of Triangle 2 are scaled by a factor of \(\frac{5}{2}\) compared to Triangle 1. We can apply this scale factor to the long leg (16 cm) of Triangle 1 to find \(x\):

\[
x = 16 \times \frac{5}{2} = 16 \times 2.5 = 40 \, \text{cm}
\]

Thus, the length of side \(x\) is **40 cm**.

Would you like further details or have any other questions? Here are some related questions you could explore:

1. How can we verify that the triangles are indeed similar?
2. How would you find the area of both triangles?
3. What is the ratio of the areas of Triangle 1 and Triangle 2?
4. If the short leg of Triangle 1 was increased, how would that affect the dimensions of Triangle 2?
5. How does the Pythagorean theorem apply to both triangles?

**Tip**: When working with similar triangles, remember that all corresponding angles are equal, and corresponding sides are proportional.

What is the length of side x in Triangle 2, which is a scale drawing of Triangle 1?

Learn how to find the length of a missing side in similar triangles using proportions. In this problem, Triangle 2 is a scale drawing of Triangle 1, and the proportional relationship between their sides helps solve for the unknown side. Suitable for students in Grades 7-8.

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