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D and E are two points respectively on sides AB and AC of triangle ABC

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Manager
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Joined: 10 Jan 2010
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D and E are two points respectively on sides AB and AC of triangle ABC  [#permalink]

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New post 23 Apr 2011, 08:44
1
13
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A
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D
E

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Question Stats:

66% (01:55) correct 34% (02:57) wrong based on 156 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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Posts: 6786
Re: D and E are two points respectively on sides AB and AC of triangle ABC  [#permalink]

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New post 07 Feb 2015, 08:17
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2
sagarag wrote:
Can somebody help understanding why A is not a right answer..
Thanks in advance

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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Re: D and E are two points respectively on sides AB and AC of triangle ABC  [#permalink]

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New post 23 Apr 2011, 10:12
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

Answer - B
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Re: D and E are two points respectively on sides AB and AC of triangle ABC  [#permalink]

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New post 07 Feb 2015, 07:37
Can somebody help understanding why A is not a right answer..
Thanks in advance
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Re: D and E are two points respectively on sides AB and AC of triangle ABC  [#permalink]

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