Sides of Similar Figures Quick Check
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Question
Use the image to answer the 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
200
200
100
100
78
78
25
To find the length of TE, we can use the concept of similarity of triangles.
The ratio of corresponding sides in similar triangles is equal.
In this case, we can set up the proportion:
(Length of TE)/(Length of LA) = (Length of NT)/(Length of AK)
Plugging in the given values, we have:
(Length of TE)/8 = (Length of NT)/5
Cross-multiplying, we get:
(Length of TE) = (Length of NT) * 8/5
We are given that EN = 125, so the length of NT is 125.
Substituting this value, we can solve for TE:
TE = 125 * 8/5
TE = 200
Therefore, the length of TE is 200.