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# In the figure above, if AB = 5, AC = 3 and BC = CD, then BE =

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Math Expert
Joined: 02 Sep 2009
Posts: 55150
In the figure above, if AB = 5, AC = 3 and BC = CD, then BE =  [#permalink]

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15 Aug 2017, 02:23
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Difficulty:

55% (hard)

Question Stats:

86% (02:01) correct 14% (01:41) wrong based on 51 sessions

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In the figure above, if AB = 5, AC = 3 and BC = CD, then BE =

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Attachment:

2017-08-15_1321.png [ 8.39 KiB | Viewed 1017 times ]

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Re: In the figure above, if AB = 5, AC = 3 and BC = CD, then BE =  [#permalink]

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15 Aug 2017, 02:29
Similar triangles with all angles equal.
Sides must be proportional
AC = CE (since BC = CD)
BE= 4-3=1
A
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: In the figure above, if AB = 5, AC = 3 and BC = CD, then BE =  [#permalink]

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18 Aug 2017, 09:13
Bunuel wrote:

In the figure above, if AB = 5, AC = 3 and BC = CD, then BE =

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

We see that triangle ABC and triangle CED are similar because they both have a 90-degree angle and angle x.

Since AB = 5 and AC = 3, BC must be 4, and thus CD must be 4 also.

So, we see that the ratio between sides of ABC and CED is: 1/1. So, since AC = 3, CE = 3, and thus BE is 4 - 3 = 1.

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Re: In the figure above, if AB = 5, AC = 3 and BC = CD, then BE =   [#permalink] 18 Aug 2017, 09:13
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