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In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the

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Magoosh GMAT Instructor
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In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

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New post 18 Dec 2014, 15:27
1
3
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (02:29) correct 34% (03:03) wrong based on 88 sessions

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similar triangle diagram.JPG
similar triangle diagram.JPG [ 15.8 KiB | Viewed 1880 times ]

In the diagram above, BD = 5, CD = 10, and AE = 40. What is the area of the shaded region?
(A) 175
(B) 350
(C) 775
(D) 1150
(E) 1575


For a set of practice problems on Similar Geometric Figures, as well as the OE for this particular problem, see:
http://magoosh.com/gmat/2014/gmat-pract ... c-figures/

Mike :-)

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Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

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New post 31 Mar 2019, 03:14
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IMO E

As the two trinagles are similar

(area of big triangle x )/(area of small triangle y) = (ratio of corresponding sides)^2

x/25 = (8/1)^2


x = 64*25 = 1600

so area of shaded region = 1600-25 = 1575


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Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

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New post 30 Apr 2019, 13:36
1
BDC=CAE ( both are 90*), BCD=ACE (common angle in 2 triangles)
Obviously remaining angles gonna be equal.

TannyaChabbra wrote:
how do you conclude that they are similar triangles ? because either its SAS, AAA or SSS but here from the given question we know only one angle is equal? kindly help.
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Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

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New post 18 Dec 2014, 15:33
These are similar triangles, but small one is reversed. After noticing that, question is easily solved by proportion:
AE/BD=AC/CD=8/1

40*10*8/2 (area of big triangle) - 5*10/2 = 1575

Answer E
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In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

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New post 19 Dec 2014, 10:10
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Triangle BCD is similar to Triangle ACE having one right angle and one common angle.
Ratio of sides is 1:8, thus ratio of Area will be 1:64.

Area of BCD = (5*10)/2= 25
Area of ACE = 64*(Area of BCD) = 64*25 = 1600

Area of shaded region = Area of ACE - Area of BCD = 1600 - 25 = 1575

Answer E
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Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

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New post 31 Mar 2019, 02:47
How do you know that Two triangles are in ratio 1 to 8? If you take CD to be as like side with AE, the two triangles will be in ratio 1 to 4.
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Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

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New post 30 Apr 2019, 09:42
how do you conclude that they are similar triangles ? because either its SAS, AAA or SSS but here from the given question we know only one angle is equal? kindly help.
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Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the   [#permalink] 30 Apr 2019, 09:42
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