Since triangle NTE is similar to triangle KLA, we can set up a proportion based on their corresponding side lengths.
The sides TE and LA correspond to each other, and the sides EN and AK correspond to each other. Thus, we have the following proportion:
\[ \frac{TE}{LA} = \frac{EN}{AK} \]
We know the following values:
- \( TE = 99 \)
- \( EN = 63 \)
- \( AK = 7 \)
Substituting these values into the proportion gives:
\[ \frac{99}{LA} = \frac{63}{7} \]
Next, we can simplify the right side:
\[ \frac{63}{7} = 9 \]
Now, the equation becomes:
\[ \frac{99}{LA} = 9 \]
To find \( LA \), we can cross-multiply:
\[ 99 = 9 \cdot LA \]
Now, we solve for \( LA \):
\[ LA = \frac{99}{9} = 11 \]
Therefore, the length of \( LA \) is
\[ \boxed{11} \]
6 answers