https://file.aiquickdraw.com/mathbot/file/1727183057859xj6qmfu2.jpg

The two triangles in the image appear to be similar, as their corresponding angles and sides seem proportional. 

### Step 1: Set up the proportion
Since the triangles are similar, the ratio of corresponding sides is equal. From the image:

- In triangle \( \triangle BHN \):
  - \( BH = 2B \)
  - \( HN = 3x - 7 \)
  
- In triangle \( \triangle RYL \):
  - \( RY = x + 11 \)
  - \( YL = 21 \)

We can set up the following proportion between corresponding sides:
\[
\frac{2B}{x + 11} = \frac{3x - 7}{21}
\]

### Step 2: Solve the proportion
Now, cross-multiply to solve for \(x\):

\[
2B \cdot 21 = (x + 11)(3x - 7)
\]

\[
42B = (x + 11)(3x - 7)
\]

Expand the right-hand side:
\[
42B = 3x^2 - 7x + 33x - 77
\]

Simplify:
\[
42B = 3x^2 + 26x - 77
\]

### Step 3: Further steps

To move forward, I'll need to clarify what value corresponds to \( B \), as it seems to represent a variable in the given problem. Could you clarify if \( B \) is a given number or if you have more context?

Let me know if you'd like more details on this step or if we should assume a value for \( B \).

Solve for x in the given similar triangles BHN and RYL.

Learn how to solve for x in a problem involving similar triangles BHN and RYL. The solution uses algebraic principles like proportions and quadratic expansion. Suitable for students in Grades 9-11.

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