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The image you've uploaded appears to be a geometry problem. It seems to be about a triangle with points \( A \), \( B \), \( C \), and \( D \), and there is a line \( DE \) that is part of the triangle. The given ratio \( AD : BD = 3 : 1 \), along with the length \( DE = 15 \) cm, asks for the length of side \( BC \).

We can apply the properties of similar triangles to solve this. Based on the provided ratio, the triangle formed by points \( A \), \( D \), and \( B \) is divided in the given ratio \( 3 : 1 \). This indicates that there is proportionality between the segments of the triangle, and this can help us find the unknown length of side \( BC \).

Let's go step by step through the process:

1. **Understanding Proportions**: The line \( DE \) is parallel to side \( BC \), and the ratio \( AD : BD = 3 : 1 \) means that \( \frac{AD}{BD} = 3 \). This suggests that the triangles formed by \( A, D, B \) and \( B, D, C \) are similar.
   
2. **Using the Properties of Similar Triangles**: Since the triangles are similar, the ratio of corresponding sides must be equal. That is:
   \[
   \frac{AD}{BD} = \frac{AE}{EC} = \frac{DE}{BC}
   \]

3. **Solving for \( BC \)**: From the above proportion, we know that:
   \[
   \frac{DE}{BC} = \frac{AD}{BD}
   \]
   Substituting the known values:
   \[
   \frac{15}{BC} = \frac{3}{1}
   \]
   Solving for \( BC \):
   \[
   BC = \frac{15 \times 1}{3} = 5 \times 3 = 15
   \]

However, the solution doesn't match the options, so I may have misinterpreted the problem setup. Would you like to review or clarify the method? Feel free to ask!

Jika AD : BD = 3 : 1, panjang DE = 15 cm, maka panjang BC adalah ....

Learn how to solve a geometry problem involving similar triangles and proportions. The problem asks for the length of side BC given the ratio of AD to BD and the length of DE. This problem is suitable for students in Grades 7-9.

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