https://file.aiquickdraw.com/mathbot/file/17297972181252hs3f0av.jpg

What is the value of x in centimeters?
A.12
B.13.5
C.9
D.9.5

The two shapes in the image are pentagons, and they appear to be similar polygons, which means their corresponding sides are proportional. 

Given:
- The side lengths of the smaller pentagon are \( 6 \, \text{cm} \), \( 9 \, \text{cm} \), and the corresponding sides in the larger pentagon are \( 9 \, \text{cm} \) and \( x \, \text{cm} \).
  
### Step-by-step solution:

1. First, identify corresponding sides. The \( 6 \, \text{cm} \) side of the smaller pentagon corresponds to the \( 9 \, \text{cm} \) side of the larger pentagon.
   
2. Set up a proportion using the corresponding sides:
   \[
   \frac{9}{6} = \frac{x}{9}
   \]

3. Solve for \( x \):
   \[
   \frac{9}{6} = \frac{x}{9}
   \]
   Cross-multiply:
   \[
   9 \times 9 = 6 \times x
   \]
   \[
   81 = 6x
   \]
   Divide both sides by 6:
   \[
   x = \frac{81}{6} = 13.5
   \]

Thus, the value of \( x \) is **13.5 cm**, so the correct answer is **B**.

Would you like further details or explanations on any step?

### Related questions:
1. What is the perimeter of each pentagon?
2. How do you find the area of a regular pentagon?
3. How can you determine whether two polygons are similar?
4. If a pentagon has side lengths increasing by a certain ratio, how do you find the ratio?
5. How do you calculate the angles in a regular pentagon?

### Tip:
Always check if two polygons are similar before applying proportions; similarity requires both equal angles and proportional corresponding sides.

What is the value of x in centimeters? A. 12 B. 13.5 C. 9 D. 9.5

Learn how to find the missing side length of a pentagon using proportions. In this geometry problem, we use the theorem of similar polygons and set up a proportion to solve for x. Suitable for students in Grades 8-10.

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