Explanation
Correct answer: B.
Choice B is correct. Since , , and are parallel, the parallel lines cut transversals and proportionally. By the proportional segments theorem, the ratio of segments on one transversal equals the ratio of corresponding segments on the other transversal. Let represent the length of . It follows that , or . Multiplying both sides of this equation by and by yields , or . Dividing both sides of this equation by yields , which to the nearest tenth is .
Desmos solution:
Note: The parallel segments create similar triangles, so the proportion finds ED before the purple expression rounds it to the nearest tenth.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect and may result from setting up the proportion incorrectly as , yielding , which gives .
Choice C
Choice C is incorrect and may result from incorrectly setting up the proportion as (inverting the right side), yielding , which gives , or from calculation errors when solving the correct proportion.
Choice D
Choice D is incorrect and may result from adding AB and FE instead of using them in a proportion, yielding , or from incorrectly setting up the proportion as , yielding , which gives , not 19.6.