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Manager  Joined: 10 Jan 2010
Posts: 95
GPA: 4
WE: Programming (Computer Software)
D and E are two points respectively on sides AB and AC of triangle ABC  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 67% (02:07) correct 33% (02:43) wrong based on 164 sessions

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D and E are two points respectively on sides AB and AC of triangle ABC such that DE is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium DECB is 25:144 and DE=5 cm, then find the length of BC.

A. 12
B. 13
C. 14
D. 11
E. 15

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Math Expert V
Joined: 02 Aug 2009
Posts: 7756
Re: D and E are two points respectively on sides AB and AC of triangle ABC  [#permalink]

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sagarag wrote:
Can somebody help understanding why A is not a right answer..

hi sagar A is not the right answer and B is the answer ..
we have a triangle ABC with a line DE parallel to BC..
now we have a triangle ADE on top and trapezium DECB below it...
the ratio of "area of triangle ADE/ area of triangle ABC"="area of triangle ADE/(area of triangle ADE+area of trapezium DECB)"
= 25/(25+144)=25/169..
now ABC and ADE are similar triangles.. so their areas ratio will be square of ratio of their similar sides..
ratio of areas = 25/169 so ratio of sides = 5/13..
DE is given 5 and corresponding sides is BC , meaning DE/BC=5/13..
DE is 5 so BC = 13 ans
hope it helped
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Manager  Joined: 11 Dec 2010
Posts: 106
WE: Consulting (Consulting)
Re: D and E are two points respectively on sides AB and AC of triangle ABC  [#permalink]

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maheshsrini wrote:
D & E are two points on sides AB & AC of triangle ABC such that DE is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium DECB is 25:144 and DE is 5 cm, then find the length of BC
a) 12 b) 13 c) 14 d) 11 e) 15

ABC and ADE are similar triangles.
So (side of ABC/side of ADE)^2=169/25
side of ABC/side of ADE = 13/5

So the length of BC = 13

Intern  Joined: 13 May 2014
Posts: 21
GMAT Date: 11-01-2014
Re: D and E are two points respectively on sides AB and AC of triangle ABC  [#permalink]

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Can somebody help understanding why A is not a right answer..
Non-Human User Joined: 09 Sep 2013
Posts: 11396
Re: D and E are two points respectively on sides AB and AC of triangle ABC  [#permalink]

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_________________ Re: D and E are two points respectively on sides AB and AC of triangle ABC   [#permalink] 03 Jan 2018, 04:54
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