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In triangle ABC, AD = DB , DE is parallel to BC, and the area of trian

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In triangle ABC, AD = DB , DE is parallel to BC, and the area of trian  [#permalink]

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New post 12 May 2016, 01:55
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

54% (01:07) correct 46% (01:16) wrong based on 111 sessions

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In triangle ABC, AD = DB , DE is parallel to BC, and the area of triangle ABC is 40. What is the area of triangle ADE ?

A. 10
B. 15
C. 20
D. 30
E. it cannot be determined from the information given


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Re: In triangle ABC, AD = DB , DE is parallel to BC, and the area of trian  [#permalink]

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New post 12 May 2016, 03:42
1
IMO A

Since DE divides the two sides in equal ratios (bec DE is II to BC) then DE=1/2of BC. So ratio of the areas are equal to square of the sides i.e DE^2/BC^2= Area ADE/Area ABC
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Re: In triangle ABC, AD = DB , DE is parallel to BC, and the area of trian  [#permalink]

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New post 03 Apr 2017, 09:49
Since Area = 40, bh=80.

(AB)(BC) = bh of the larger triangle.

AD=DB; AD=1/2AB
DE is parallel to BC, hence DE=1/2BC

Area of smaller triangle = bh/2
=(1/2AB)(1/2BC)(1/2)
=80/8
=10

Answer is A.
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Re: In triangle ABC, AD = DB , DE is parallel to BC, and the area of trian  [#permalink]

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New post 17 Jul 2018, 22:46
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Re: In triangle ABC, AD = DB , DE is parallel to BC, and the area of trian &nbs [#permalink] 17 Jul 2018, 22:46
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