Sides of Similar Figures Practice
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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 63, side upper T upper E is on the right labeled as 99, 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 that is labeled as 7, side upper L upper A is on the right labeled as x, and side upper K upper L is on the left and is not labeled.
Triangle NTE
is similar to triangle KLA
. If TE=
99, EN=
63, and AK=
7, what is the length of LA
?
(1 point)
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page 12 of 13
To find the length of LA, we can use the concept of similarity of triangles.
In similar triangles, corresponding sides are proportional. This means that the ratio of the lengths of corresponding sides in the larger triangle to the lengths of corresponding sides in the smaller triangle are equal.
Here, we have:
TE = 99
EN = 63
AK = 7
We want to find LA.
By setting up a proportion:
(Triangle NTE / Triangle KLA) = (TE / AK) = (EN / LA)
Substituting the given values:
(99 / 7) = (63 / LA)
Now, we can cross multiply to solve for LA:
99 * LA = 7 * 63
99LA = 441
LA = 441 / 99
LA = 4.45
Therefore, the length of LA is approximately 4.45.