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The problem describes two similar triangles, \( \triangle ABC \) and \( \triangle DEF \), where the lengths of the sides of triangle \( ABC \) are given as:

- \( AB = 16.6 \, \text{cm} \)
- \( BC = 21.6 \, \text{cm} \)
- \( AC = 26.6 \, \text{cm} \)

The similarity ratio (or scaling factor) between the two triangles is given as \( 0.5 \). This means that each side of triangle \( DEF \) will be half the corresponding side of triangle \( ABC \).

To find the side lengths of \( \triangle DEF \), we can multiply the sides of \( \triangle ABC \) by the ratio \( 0.5 \).

Let's calculate the sides of \( \triangle DEF \):

1. \( DE = 0.5 \times AB = 0.5 \times 16.6 \)
2. \( EF = 0.5 \times BC = 0.5 \times 21.6 \)
3. \( DF = 0.5 \times AC = 0.5 \times 26.6 \)

I'll calculate the results next.Here are the calculations for the side lengths of triangle \( DEF \):

1. \( DE = 0.5 \times 16.6 = 8.3 \, \text{cm} \)
2. \( EF = 0.5 \times 21.6 = 10.8 \, \text{cm} \)
3. \( DF = 0.5 \times 26.6 = 13.3 \, \text{cm} \)

Thus, the side lengths of triangle \( DEF \) are:

- \( DE = 8.3 \, \text{cm} \)
- \( EF = 10.8 \, \text{cm} \)
- \( DF = 13.3 \, \text{cm} \)

Would you like more details or have any questions? Here are five related questions you might find helpful:

1. What does it mean for two triangles to be similar?
2. How do we calculate the ratio of similarity between two triangles?
3. Can we find the angles of triangle \( DEF \) based on the given information?
4. What other properties of similar triangles can be determined besides side lengths?
5. How does scaling affect the area of two similar triangles?

**Tip:** When two triangles are similar, their corresponding angles are equal, and their sides are proportional by the similarity ratio.

Trijstūris ABC ir līdzīgs trijstūrim DEF. Zināms, ka AB = 16.6 cm, BC = 21.6 cm un AC = 26.6 cm, līdzības koeficients ir 0.5. Aprēķini trijstūra DEF malas!

This problem involves calculating the sides of triangle DEF, which is similar to triangle ABC. Given AB = 16.6 cm, BC = 21.6 cm, and AC = 26.6 cm with a similarity ratio of 0.5, the solution walks through using proportions to find DE, EF, and DF. Suitable for students in Grades 6-8.

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