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Question

An illustration shows a larger triangle upper N upper T upper E and a smaller triangle upper K upper L upper A, with labeled sides. On the first triangle, side upper E upper N is the base labeled as 125, side upper T upper E is on the right labeled as x, and side upper N upper T is on the left and is not labeled. On the second triangle, side upper A upper K is the base and is labeled as 5, side upper L upper A is on the right labeled as 8, and side upper K upper L is on the left and is not labeled.

Triangle NTE
is similar to triangle KLA
. If LA=
8, EN=
125, and AK=
5, what is the length of TE
?

(1 point)
Responses

25
25

200
200

100
100

78
78
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Answer 1

To find the length of side \( TE \) in triangle \( NTE \), we can use the property of similar triangles. The triangles are similar, which means the ratios of their corresponding sides are equal.

Given:

• \( EN = 125 \) (base of triangle \( NTE \))
• \( LA = 8 \) (base of triangle \( KLA \))
• \( AK = 5 \) (side of triangle \( KLA \))
• \( TE = x \) (the side we want to find in triangle \( NTE \))

Using the similarity ratio, we can write:

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

Substituting the known values into the proportion:

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

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

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

\[ 625 = 8x \]

Now, divide both sides by 8:

\[ x = \frac{625}{8} = 78.125 \]

Since the question likely asks for a rounded length, \( TE \approx 78 \).

Thus, the closest answer is:

78