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Answer:
Step-by-step explanation:
The given parallel lines mean that the two triangles are similar:
∆FDE ~ ∆FLK
That means corresponding sides are proportional.
FE/FK = ED/KL
FE = FK(ED/KL) = 4(15/6) = 10
and
FL/FD = KL/ED
FL = FD·KL/ED = 12(6/15) = 12(2/5) = 4.8
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Additional comment
Each of the diagonal lines, LD and KE, can be considered to be transversals between the parallel lines DE and KL. This means the interior angles at either end of those diagonals will be congruent. Hence the triangles are similar by the AA postulate.
