The task in the image is about two similar triangles, $\triangle ABC$ and $\triangle DEF$. We are given:

• $AB = 8.3 \, \text{cm}$,
• $BC = 13.3 \, \text{cm}$,
• $AC = 18.3 \, \text{cm}$,
• The similarity coefficient (scale factor) between the two triangles is $0.5$.

Since the triangles are similar, the sides of $\triangle DEF$ are proportional to the sides of $\triangle ABC$ by the given coefficient $0.5$.

Let's calculate the side lengths of $\triangle DEF$:

$DE = 0.5 \times AB = 0.5 \times 8.3 \, \text{cm} = 4.15 \, \text{cm},$ $EF = 0.5 \times BC = 0.5 \times 13.3 \, \text{cm} = 6.65 \, \text{cm},$ $DF = 0.5 \times AC = 0.5 \times 18.3 \, \text{cm} = 9.15 \, \text{cm}.$

Therefore, the side lengths of triangle $DEF$ are:

• $DE = 4.15 \, \text{cm}$,
• $EF = 6.65 \, \text{cm}$,
• $DF = 9.15 \, \text{cm}$.

Would you like more details on this solution or have any questions? Here are some related questions for practice:

1. What is the ratio of areas of similar triangles if the scale factor is 0.5?
2. How do you calculate the perimeters of similar triangles using their scale factor?
3. What are the criteria for two triangles to be similar?
4. How does the scale factor affect the angles in similar triangles?
5. Can two triangles with different angles still be similar?

Tip: In similar triangles, corresponding angles are always equal, and the sides are proportional according to a constant ratio.