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We are given two similar triangles, \( \triangle EFG \) and \( \triangle HIJ \), and we need to find the length of \( HI \) (denoted as \( x \)) in \( \triangle HIJ \).

### Step 1: Identify Corresponding Sides
Since the triangles are similar, the sides of the triangles are proportional. We are given:
- \( EF = 23 \)
- \( FG = 11 \)
- \( IJ = 54 \)
- \( HI = x \)

So, the corresponding sides are:
- \( EF \) corresponds to \( IJ \)
- \( FG \) corresponds to \( HI \)

### Step 2: Set Up the Proportion
Using the fact that the ratios of corresponding sides are equal, we set up the proportion:
\[
\frac{EF}{IJ} = \frac{FG}{HI}
\]
Substituting the known values:
\[
\frac{23}{54} = \frac{11}{x}
\]

### Step 3: Solve for \( x \)
Cross-multiply to solve for \( x \):
\[
23x = 11 \times 54
\]
\[
23x = 594
\]
\[
x = \frac{594}{23}
\]
\[
x \approx 25.8
\]

So, the length of \( HI \) is approximately **25.8** units.

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Would you like more details or explanations on any part of the process? Here are five related questions you could explore:

1. How do you prove that two triangles are similar?
2. What other properties do similar triangles share?
3. How would the solution change if we had additional angles given?
4. Can this method be used if only part of the information was given?
5. What are some real-life applications of similar triangles?

**Tip:** Always verify that you are comparing corresponding sides correctly when working with similar triangles.

Triangle EFG is similar to triangle HIJ. Find HI. Round your answer to the nearest tenth if necessary.

Solve for the missing side HI in triangle HIJ, which is similar to triangle EFG. Learn about proportions and the theorem of similar triangles in this geometry problem. The given sides are EF = 23, FG = 11, and IJ = 54.

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