We are given two similar triangles in the image, and we need to find the unknown side lengths $x$ and $y$.

To solve this, we use the property of similar triangles: corresponding sides of similar triangles are proportional. This means we can set up ratios between corresponding sides of the two triangles.

Given:

• First triangle: sides are 6.5 m, 8.5 m, and 13.5 m.
• Second triangle: sides are $x$, 15.6 m, and $y$.

Step 1: Find $x$

Let's set up a ratio for the corresponding sides: $\frac{x}{8.5} = \frac{15.6}{13.5}$

Now solve for $x$: $x = \frac{15.6}{13.5} \times 8.5$ $x = 9.82 \, \text{m}$

Step 2: Find $y$

Similarly, we set up a ratio for the corresponding sides: $\frac{y}{13.5} = \frac{15.6}{13.5}$

Since the larger triangle is scaled by the same factor: $y = 15.6 \, \text{m}$

Final Answers:

• $x = 9.82 \, \text{m}$
• $y = 15.6 \, \text{m}$

Would you like more details on these steps or any clarifications?

Here are 5 related questions to expand on this topic:

1. How do we know the triangles are similar?
2. Can similar triangles have sides that are in different proportions?
3. What would happen if only two sides of the triangles were given—can we still find the missing lengths?
4. Why does the proportionality hold for all corresponding sides in similar triangles?
5. How do we determine which sides of two triangles are corresponding?

Tip: Always ensure that corresponding sides in similar triangles are paired correctly when setting up proportions.