there are two similar  triangles, with the smaller triangle having sides  with lengths  of 3cm, 4cm, and 5cm. If the smallest  side  of the larger triangle  is 7cm long, how long will the other two sides be?

To find the lengths of the other two sides of the larger triangle, we can use the property of similar triangles, which states that corresponding sides of similar triangles are proportional.

Given:
- Smaller triangle sides: 3 cm, 4 cm, and 5 cm.
- Larger triangle's smallest side: 7 cm.

### Step 1: Determine the ratio of similarity
The smallest side of the smaller triangle is 3 cm, and the smallest side of the larger triangle is 7 cm.

The ratio of similarity (scaling factor) is:
\[
\text{Ratio} = \frac{7 \text{ cm}}{3 \text{ cm}} = \frac{7}{3}
\]

### Step 2: Find the lengths of the other two sides of the larger triangle
- **Second side:**
\[
\text{Second side} = 4 \text{ cm} \times \frac{7}{3} = \frac{28}{3} \text{ cm} \approx 9.33 \text{ cm}
\]
- **Third side:**
\[
\text{Third side} = 5 \text{ cm} \times \frac{7}{3} = \frac{35}{3} \text{ cm} \approx 11.67 \text{ cm}
\]

### Final Answer:
The lengths of the other two sides of the larger triangle are approximately **9.33 cm** and **11.67 cm**.

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

Here are 5 related questions to further your understanding:

1. What is the importance of the ratio of similarity in similar triangles?
2. How do you prove that two triangles are similar?
3. How does the Pythagorean theorem apply to the smaller triangle?
4. If the perimeter of the larger triangle is given, how can you find the exact scaling factor?
5. How do the angles of similar triangles compare?

**Tip:** When working with similar triangles, always ensure that you correctly identify corresponding sides to apply the ratio of similarity accurately.

Learn how to find the lengths of the other two sides of a larger triangle using properties of similar triangles. Given the smaller triangle with sides 3 cm, 4 cm, and 5 cm, and the smallest side of the larger triangle as 7 cm, discover the proportional relationships and calculations involved. Suitable for Grades 7-9.

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