Question

\delta lmn \sim \delta lfe

what is nl?

Explanation:

⚡ Using what you learned: similarity criteria for triangles

Step 1: Identify corresponding sides

The problem states that:

$$ \Delta LMN \sim \Delta LFE $$

From the similarity statement, we match the corresponding vertices and sides:

• Side \( LM \) corresponds to side \( LF \).
• Side \( LN \) corresponds to side \( LE \).

From the given image:

• \( LM = 24 \)
• \( LF = 4 \)
• \( LE = 6 \)
• \( LN = ? \)

Step 2: Set up the proportion

Using the ratio of corresponding sides:

$$ \frac{LN}{LE} = \frac{LM}{LF} $$

Substitute the known values:

$$ \frac{NL}{6} = \frac{24}{4} $$

Step 3: Solve for NL

Simplify the ratio on the right side:

$$ \frac{NL}{6} = 6 $$

Multiply both sides by 6:

$$ NL = 6 \times 6 $$

$$ NL = 36 $$

Answer:

36