https://file.aiquickdraw.com/mathbot/file/1729710935725q3ec2adz.jpg

What is the length of BC¯¯¯¯¯¯¯¯
 in centimeters?
A.21
 cm
B.12
 cm
C.20
 cm
D.10
 cm

In the given image, we have two pentagons. One is smaller (pentagon \( JKNML \)) and the other is larger (pentagon \( ABCDE \)). You are asked to find the length of side \( BC \) in the larger pentagon.

### Approach:
- The smaller pentagon has side lengths of 5 cm and 7 cm, as indicated on sides \( JK \) and \( KL \).
- The larger pentagon has one side, \( AB \), given as 15 cm. We are tasked with determining the length of \( BC \).
  
These two pentagons are similar (since they have the same shape and are regular), which means their corresponding sides are proportional.

We know:
- \( JK = 5 \, \text{cm} \) corresponds to \( AB = 15 \, \text{cm} \).
- The ratio of the sides is therefore \( \frac{AB}{JK} = \frac{15}{5} = 3 \).

Since \( BC \) corresponds to side \( KL = 7 \, \text{cm} \) in the smaller pentagon, we can calculate \( BC \) using the same ratio:

\[
BC = KL \times 3 = 7 \times 3 = 21 \, \text{cm}.
\]

Thus, the length of \( BC \) is **21 cm**, which corresponds to option **A**.

Would you like more details on this solution or have any further questions?

### Follow-up Questions:
1. How do we verify that two polygons are similar?
2. What are the properties of regular pentagons?
3. Can you calculate the perimeter of both pentagons based on the information given?
4. How would the solution change if only one side of the pentagon was known?
5. What would be the ratio of their areas given the scale factor of their sides?

### Tip:
In similar polygons, the ratio of corresponding side lengths is the same as the ratio of their perimeters, and the square of this ratio gives the ratio of their areas.

What is the length of BC¯¯¯¯¯¯¯¯ in centimeters?

Discover how to find the length of side BC in a pair of similar pentagons using proportions. This solution involves applying the concept of similar polygons, proportional sides, and calculating BC based on the given dimensions of the pentagons. Suitable for students in Grades 7-9.

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