Question in-the
In the figure above, 
, 
, and 
are parallel. Points B and E lie on 
and 
, respectively. If 
, and 
, what is the length of 
, to the nearest tenth?
16.8
17.5
18.4
19.6
In the figure above, , , and are parallel. Points B and E lie on and
Medium-difficulty · SAT Math · Lines, Angles, and Triangles — Angle relationships (parallel lines). Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice B is correct. Since 
, 
, and 
are parallel, quadrilaterals 
and 
are similar. Let x represent the length of . With similar figures, the ratios of the lengths of corresponding sides are equal. It follows that 
. Multiplying both sides of this equation by 18.5 and by x yields 
, or 
. Dividing both sides of this equation by 9 yields 
, which to the nearest tenth is 17.5.
Choices A, C, and D are incorrect and may result from errors made when setting up the proportion.
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