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We are given that pentagon \( JKLNM \) is similar to pentagon \( ABCDE \), and we're asked to find the length of side \( BC \) in the larger pentagon.

### Key Information:
- Side \( JK \) in pentagon \( JKLNM \) measures 5 cm.
- Side \( AB \) in pentagon \( ABCDE \) measures 15 cm.
- Side \( KL \) in pentagon \( JKLNM \) measures 7 cm.
- We are asked to find the length of side \( BC \).

### Similarity of Pentagons:
Since the two pentagons are similar, corresponding sides of the pentagons are proportional. This means the ratio of corresponding sides in the smaller pentagon to the larger pentagon is constant.

We can calculate this ratio using the sides \( JK \) and \( AB \):
\[
\text{Ratio} = \frac{JK}{AB} = \frac{5}{15} = \frac{1}{3}
\]
This means that each side in pentagon \( ABCDE \) is three times the length of the corresponding side in pentagon \( JKLNM \).

### Finding \( BC \):
Side \( KL \) in pentagon \( JKLNM \) corresponds to side \( BC \) in pentagon \( ABCDE \). Using the ratio:
\[
BC = 3 \times KL = 3 \times 7 = 21 \, \text{cm}
\]

Thus, the length of \( BC \) is **21 cm**, so the correct answer is **D.**.

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Do you need further details or have any questions?

Here are some related questions to expand your understanding:

1. How do you find the scale factor between two similar polygons?
2. How would the answer change if the ratio between the pentagons were different?
3. Can the angles in two similar polygons ever be different?
4. How does proportionality help in solving problems involving similar shapes?
5. How would you use a similar approach to find the perimeter of one pentagon if the other pentagon's perimeter is known?

**Tip:** When solving problems with similar shapes, always identify corresponding sides and use proportional relationships to find missing values.

Pentagon JKLNM is similar to pentagon ABCDE. What is the length of BC in centimeters?

Solve a geometry problem where two similar pentagons are compared, and the length of side BC is found using proportions and similarity theorems. Includes step-by-step solution and explanation. Suitable for students in Grades 7-10.

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