triangle NTE is similar to triangle KLA if LA=8, EN =125 and AK=5 what is the length of TE
A. 78
B.25
C.100
D. 200
To determine the length of TE, we first need to find the scale factor between the two similar triangles.
The ratio of the corresponding sides of two similar triangles is equal to the scale factor.
Let x be the length of TE.
To find the scale factor, we can compare the corresponding sides:
NT / KL = TE / LA
NTE is similar to KLA, so NT is proportional to KL. We have NT = EN + TE and KL = AK + LA.
So, EN + TE / AK + LA = TE / LA
125 + x / 5 + 8 = x / 8
125 + x / 13 = x / 8
8(125 + x) = 13x
1000 + 8x = 13x
5x = 1000
x = 200
Therefore, the length of TE is 200.
So, the answer is D. 200.