Question

Triangle NTE is similar to triangle KLA . If LA= 8, EN= 125, and AK= 5, what is the length of TE ? (1 point) Responses 200 200 78 78 25 25 100

Answer 1

Since triangle NTE is similar to triangle KLA, the corresponding sides are proportional.

This gives us the proportions:

\[ \frac{EN}{LA} = \frac{TE}{AK} \]

Substituting the values you provided:

- \( EN = 125 \)
- \( LA = 8 \)
- \( AK = 5 \)

We can set up the proportion as follows:

\[ \frac{125}{8} = \frac{TE}{5} \]

Now we can cross-multiply to solve for \( TE \):

\[ 125 \cdot 5 = 8 \cdot TE \]

This simplifies to:

\[ 625 = 8 \cdot TE \]

Now, divide both sides by 8:

\[ TE = \frac{625}{8} \]

Calculating that gives:

\[ TE = 78.125 \]

Since the answer choices provided are whole numbers, we can round \( TE \) to the closest whole number, which is 78.

So, the length of TE is **78**.