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# In the figure above, line segment AC is parallel to line segment BD.

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Math Expert
Joined: 02 Sep 2009
Posts: 44645
In the figure above, line segment AC is parallel to line segment BD. [#permalink]

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10 Apr 2018, 00:03
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Question Stats:

80% (01:08) correct 20% (01:34) wrong based on 23 sessions

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In the figure above, line segment AC is parallel to line segment BD. If line segment AC = 15, line segment BD = 10, and line segment CE = 30, what is the length of line segment CD?

A. 10
B. 15
C. 20
D. 25
E. 30

[Reveal] Spoiler:
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Triangles_ABCDE.png [ 6.2 KiB | Viewed 224 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, line segment AC is parallel to line segment BD. [#permalink]

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10 Apr 2018, 00:14
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Given: BD = 10 | AC = 15 | CE = 30

From the above figure, we are given Angle C = D = 90. Angle E is common.
Hence, the triangles ACE and BDE are similar(AAA similarity)

In similar triangles, the ratios of the length of the corresponding sides are equal.
$$\frac{BD}{DE} = \frac{AC}{CE}$$

Substituting values
$$\frac{10}{x} = \frac{15}{30}$$ -> $$x = 10*2 = 20$$

Therefore, the length of CD = CE-DE = 30-20 = 10(Option A)
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Re: In the figure above, line segment AC is parallel to line segment BD.   [#permalink] 10 Apr 2018, 00:14
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