To solve this problem, we can set up a proportion using the corresponding sides of the two similar triangles:
NTE/KLA = TE/LA
Given that TE = 99, EN = 63, and AK = 7, we can substitute these values into the proportion:
(99)/(7) = (63)/(LA)
Now we can cross-multiply and solve for LA:
99 * LA = 7 * 63
99LA = 441
LA = 441 / 99
LA ≈ 4.45
Therefore, the length of LA is approximately 4.45.