To solve this, we need to use the concept of similar rectangles. Since the door and the window are similar, their corresponding dimensions are proportional.

Let's assume the following:

• Height of the door = $H_{\text{door}}$
• Width of the door = $W_{\text{door}}$
• Height of the window = $H_{\text{window}}$
• Width of the window = $W_{\text{window}}$

The key fact about similar rectangles is that the ratio of their corresponding dimensions (height to height and width to width) remains constant.

Thus, we have:

$\frac{H_{\text{window}}}{H_{\text{door}}} = \frac{W_{\text{window}}}{W_{\text{door}}}$

Step-by-Step Solution:

1. Identify the dimensions: Let's extract the dimensions from the problem:

   • Height of the door = 220 cm
   • Width of the door = 100 cm
   • Width of the window = 30 cm

2. Set up the proportion: Using the formula for similar rectangles, we set up the proportion as:

   $\frac{H_{\text{window}}}{220} = \frac{30}{100}$

3. Solve for $H_{\text{window}}$:

   First, simplify the ratio:

   $\frac{30}{100} = 0.3$

   Now, multiply both sides of the equation by 220 to isolate $H_{\text{window}}$:

   $H_{\text{window}} = 220 \times 0.3 = 66 \, \text{cm}$

Conclusion:

The height of the window is 66 cm, so the correct answer is A.

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Do you want any further details on this process or have any questions?

Here are 5 related questions for further practice:

1. If the width of the window was 50 cm, what would its height be?
2. What would the height of the window be if the door's height was 250 cm instead of 220 cm?
3. If the ratio of the door's height to width was 1.5, what would the height be for a window with a width of 40 cm?
4. How do we know that the door and window are similar rectangles in this context?
5. If the height of the window is given as 100 cm, what is its width assuming the door's dimensions remain the same?

Tip: When dealing with similar figures, always use proportional reasoning between corresponding sides to solve for unknown dimensions.