The problem involves two similar triangles, where you are asked to find the length of the side $h_1$ in the smaller triangle. Since the triangles are similar, the ratios of corresponding sides are equal.

Given:

• Larger triangle sides: $17.4 \, \text{cm}$ and $13.2 \, \text{cm}$
• Smaller triangle sides: $2.9 \, \text{cm}$ and $h_1$

The ratio of the corresponding sides of the triangles can be written as:

$\frac{h_1}{13.2} = \frac{2.9}{17.4}$

We can solve for $h_1$ by cross-multiplying and dividing:

$h_1 = \frac{13.2 \times 2.9}{17.4}$

Let me calculate that for you.The length of the side $h_1$ in the smaller triangle is approximately $2.2 \, \text{cm}$.

Do you need further details or have any other questions?

Here are some related questions for further exploration:

1. How would you find the area of each triangle?
2. What would be the length of $h_1$ if the larger triangle's side was 20 cm?
3. Can you use the Pythagorean theorem to find the hypotenuse of the smaller triangle?
4. How do you determine if two triangles are similar based on side lengths?
5. What is the relationship between the areas of similar triangles?

Tip: Always check if triangles are similar by comparing the ratios of their corresponding sides.