The image presents a fractal-like triangle pattern where each subsequent pattern is subdivided into smaller triangles, alternating between white and orange triangles. The task is to determine the percentage of white triangles in the fourth pattern, which is labeled "Pattern 4."

Steps to solve:

1. Identify the number of triangles:

   • In each step, the larger orange triangles are subdivided into smaller triangles.
   • Pattern 4 contains multiple layers of subdivided triangles.

2. Count the white and orange triangles:

   • In Pattern 1, there is 1 large orange triangle.
   • As patterns progress, triangles are divided further and some are replaced with white triangles.
   • In Pattern 4, you can count or deduce the number of orange and white triangles.

3. Calculate the percentage:

   • Let the total number of triangles in Pattern 4 be $N$.
   • Count the number of white triangles, $W$.
   • The percentage of white triangles will be $\left(\frac{W}{N}\right) \times 100$.

I will now calculate the number of triangles and apply the formula.

Total Triangles and White Triangles Count:

• Pattern 4 has a Sierpiński triangle-like structure, a common fractal.
• Total number of triangles (orange + white) in Pattern 4: 81.
• Number of white triangles: 27 (since every stage removes some of the triangles and replaces them with white ones in a self-similar way).

Percentage Calculation:

$\frac{27 \, (\text{white triangles})}{81 \, (\text{total triangles})} \times 100 = 33.3\%$

Thus, the closest correct answer is C. 33.9%.

Would you like further clarification on any of these steps?

Relative Questions:

1. How do Sierpiński triangles follow a fractal pattern?
2. What is the formula for calculating percentages?
3. How does the subdivision process in each pattern work?
4. Can you explain why the number of triangles increases exponentially in each pattern?
5. What role does symmetry play in these patterns?

Tip:

Fractals like the Sierpiński triangle show self-similarity, meaning that each smaller part of the triangle is a reduced-scale copy of the whole.