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To solve this proportion, we first need to convert all the units into a consistent format. We will convert the measurements in feet and inches to inches, as both feet and inches need to be expressed in a single unit.

### Step 1: Convert feet and inches to inches

- **For 2 ft 6 in:**
  - \( 2 \, \text{ft} = 2 \times 12 = 24 \, \text{inches} \)
  - So, \( 2 \, \text{ft} \, 6 \, \text{in} = 24 + 6 = 30 \, \text{inches} \).

- **For 4 ft 2 in:**
  - \( 4 \, \text{ft} = 4 \times 12 = 48 \, \text{inches} \)
  - So, \( 4 \, \text{ft} \, 2 \, \text{in} = 48 + 2 = 50 \, \text{inches} \).

Now we rewrite the proportion in terms of inches:

\[
\frac{30 \, \text{in}}{50 \, \text{in}} = \frac{2.1 \, \text{cm}}{x}
\]

### Step 2: Solve the proportion

Cross-multiply to solve for \( x \):

\[
30 \cdot x = 50 \cdot 2.1
\]

\[
30x = 105
\]

\[
x = \frac{105}{30} = 3.5 \, \text{cm}
\]

### Final Answer:
The value of \( x \) is \( 3.5 \, \text{cm} \).

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Would you like a more detailed explanation, or do you have any questions?

Here are some related questions to consider:
1. How do you convert other combinations of feet and inches to a single unit?
2. How do you solve proportions when the units are different?
3. Can you explain why cross-multiplication works in proportions?
4. How would you solve a similar problem with more complex units?
5. What if the units were mixed, such as meters and inches?

**Tip:** Always make sure to convert all units to a consistent format before solving proportions!

Solve the proportion equation: (2 ft 6 in / 4 ft 2 in) = (2.1 cm / x).

Learn how to solve the proportion equation by converting mixed units of feet and inches to a single unit and using cross-multiplication. This problem covers key concepts like unit conversion, proportions, and cross multiplication. Suitable for students in Grades 6-8.

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