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.