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The problem in the image describes the Japanese flag, where the flag's length-to-width ratio is given as 3:2, and the diameter of the red circle is \( \frac{3}{5} \) of the width of the flag. The task is to find the white area of the flag given that the length of the flag is 15 meters.

Let's break it down:

### Step 1: Determine the dimensions of the flag
- The length-to-width ratio is \( 3:2 \), and the length is 15 meters.
- Using the ratio:
  \[
  \frac{3}{2} = \frac{15}{w}
  \]
  where \( w \) is the width of the flag. Solving for \( w \):
  \[
  w = \frac{15 \times 2}{3} = 10 \, \text{meters}.
  \]

### Step 2: Calculate the area of the flag
The area \( A_{\text{flag}} \) of the rectangular flag is given by:
\[
A_{\text{flag}} = \text{length} \times \text{width} = 15 \times 10 = 150 \, \text{m}^2.
\]

### Step 3: Determine the diameter and area of the red circle
- The diameter of the red circle is \( \frac{3}{5} \) of the width of the flag. Thus:
  \[
  \text{Diameter of the circle} = \frac{3}{5} \times 10 = 6 \, \text{meters}.
  \]
- The radius \( r \) of the circle is half of the diameter:
  \[
  r = \frac{6}{2} = 3 \, \text{meters}.
  \]
- The area \( A_{\text{circle}} \) of the red circle is:
  \[
  A_{\text{circle}} = \pi r^2 = \pi \times 3^2 = 9\pi \, \text{m}^2.
  \]
  Using \( \pi \approx 3.1416 \), we can calculate:
  \[
  A_{\text{circle}} \approx 9 \times 3.1416 = 28.2744 \, \text{m}^2.
  \]

### Step 4: Calculate the white area
The white area is the area of the flag minus the area of the red circle:
\[
A_{\text{white}} = A_{\text{flag}} - A_{\text{circle}} = 150 - 28.2744 \approx 121.7256 \, \text{m}^2.
\]

Thus, the white area on the Japanese flag is approximately \( 121.73 \, \text{m}^2 \).

Would you like further clarification or additional details?

Here are five follow-up questions you might find helpful:
1. How would the result change if the flag's length were different?
2. Can you calculate the perimeter of the red circle based on the given dimensions?
3. What would the area of the white portion be if the circle's diameter were instead \( \frac{2}{3} \) of the flag's width?
4. How would you find the percentage of the flag covered by the red circle?
5. How can you verify that the length-to-width ratio is correct for a different flag size?

**Tip:** Always ensure the units in your calculations are consistent, especially when dealing with areas and lengths in different units.

Jika diketahui rasio panjang : lebar = 3 : 2 dan diameter lingkaran merah merupakan 3/5 dari lebar bendera, luas bagian putih pada bendera Jepang dengan panjang 15 m adalah ... m².

Learn how to calculate the white area on the Japanese flag, given a length-to-width ratio of 3:2 and a circle diameter that is 3/5 of the flag's width. This problem covers key geometric concepts like area of rectangles and circles and is suitable for students in Grades 9-12.

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