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```python
from PIL import Image

# Load the image to check its content
image_path = '/mnt/data/2024-12-09-17-yKKt0uiuImxRQES0gsuq.jpg'
img = Image.open(image_path)
img.show()
```
Result: run success✅
```shell
null
```

I have displayed the image you uploaded. It seems to contain a math exercise related to squares and diagonals. I will now proceed with interpreting and solving the exercise.

The problem states:

1. Hình vuông có cạnh a thì đường chéo có độ dài $a\sqrt{2}$: This means that for a square with side length \(a\), the length of the diagonal is \(a\sqrt{2}\).

2. Hình vuông có đường chéo \(4\sqrt{2}\) cm thì có chu vi là ... cm: For a square with a diagonal length of \(4\sqrt{2}\) cm, the problem asks for the perimeter.

### Step 1: Relationship Between Diagonal and Side Length of a Square
For a square, the relationship between the side length \(a\) and the diagonal \(d\) is given by the Pythagorean theorem:

\[
d = a\sqrt{2}
\]

### Step 2: Solve for the Side Length
We are told the diagonal is \(4\sqrt{2}\) cm. Therefore, using the equation above:

\[
4\sqrt{2} = a\sqrt{2}
\]

To solve for \(a\), divide both sides by \(\sqrt{2}\):

\[
a = 4 \text{ cm}
\]

### Step 3: Calculate the Perimeter
The perimeter \(P\) of a square is given by:

\[
P = 4a
\]

Since \(a = 4\) cm:

\[
P = 4 \times 4 = 16 \text{ cm}
\]

### Final Answer:
The perimeter of the square is \(16\) cm.