NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 00:05 It is currently 24 Apr 2024, 00:05
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4448
Own Kudos [?]: 28569 [12]
Given Kudos: 130
In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the [#permalink] New post   18 Dec 2014, 15:27
1
Kudos
11
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

71% (02:33) correct 29% (02:59) wrong based on 188 sessions
Hide Show timer Statistics
Attachment:
similar triangle diagram.JPG
similar triangle diagram.JPG [ 15.8 KiB | Viewed 5307 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:
https://magoosh.com/gmat/2014/gmat-pract ... c-figures/

Mike :-)
ShowHide Answer
Official Answer
E
User avatar
lolopolo
Intern
Intern
Joined: 30 Sep 2013
Posts: 23
Own Kudos [?]: 1 [1]
Given Kudos: 8
Concentration: Healthcare, Technology
Schools: Duke '17 (D) Ross '17 (WL) Kenan-Flagler '17 (A)
Send PM
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the [#permalink] New post   18 Dec 2014, 15:33
1
Kudos
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
User avatar
B
beattheheat
Manager
Manager
Joined: 20 Feb 2013
Posts: 66
Own Kudos [?]: 97 [1]
Given Kudos: 45
Location: India
Schools: IIMA (D) SPJ PGPM"16 (A)
GMAT 1: 690 Q49 V34
WE:Information Technology (Computer Software)
Send PM
In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the [#permalink] New post   19 Dec 2014, 10:10
1
Bookmarks
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
avatar
B
Akash777
Intern
Intern
Joined: 27 Apr 2016
Posts: 10
Own Kudos [?]: 1 [1]
Given Kudos: 17
Location: Japan
Schools: Darden '21
Send PM
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the [#permalink] New post   31 Mar 2019, 02:47
1
Bookmarks
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.
User avatar
G
m1033512
Senior Manager
Senior Manager
Joined: 25 Feb 2019
Posts: 280
Own Kudos [?]: 217 [2]
Given Kudos: 32
Send PM
Reviews Badge
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the [#permalink] New post   31 Mar 2019, 03:14
2
Kudos
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


Award kudos if helpful

Posted from my mobile device
avatar
B
TannyaChabbra
Intern
Intern
Joined: 19 Feb 2019
Posts: 4
Own Kudos [?]: 5 [1]
Given Kudos: 10
Send PM
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the [#permalink] New post   30 Apr 2019, 09:42
1
Bookmarks
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.
User avatar
L
nick1816
Retired Moderator
Joined: 19 Oct 2018
Posts: 1878
Own Kudos [?]: 6295 [1]
Given Kudos: 704
Location: India
Send PM
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the [#permalink] New post   30 Apr 2019, 13:36
1
Kudos
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.
User avatar
L
Fdambro294
VP
VP
Joined: 10 Jul 2019
Posts: 1392
Own Kudos [?]: 542 [0]
Given Kudos: 1656
Send PM
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the [#permalink] New post   26 Oct 2020, 23:58
Triangle CAE ~ Triangle CDB

(by the A-A Postulate)

Ratio of Corresponding Sides:

Triangle CAE : Triangle CDB = Side AE : Side DB = 40 : 5 = 8 : 1


RATIO of Areas of Similar Triangles = SQUARE of the Ratio of Corresponding Sides in its most reduced form

AREA of Triangle CAE : AREA of Triangle CDB = (8)^2 : (1)^2 = 64 : 1


Actual Area of Triangle CDB = (1/2) * 5 * 10 = 25

Given the Ratio of Areas ----> Actual Area of Triangle ACE = 25 * (64) = 1, 600


Shaded Area = Area of Triangle ACE - Area of Triangle CDB = 1,600 - 25 =

1,575


-E-
User avatar
L
Fdambro294
VP
VP
Joined: 10 Jul 2019
Posts: 1392
Own Kudos [?]: 542 [0]
Given Kudos: 1656
Send PM
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the [#permalink] New post   27 Oct 2020, 00:00
I find it easier to remember the A-A-A Postulate to prove Triangle Similarity as just the

A-A Postulate

if 2 Angles are Equal across 2 Triangles ------> the 3rd Corresponding Angle will be Equal also and the Triangles will be Similiar


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.
User avatar
B
adityasuresh
Manager
Manager
Joined: 03 May 2020
Posts: 108
Own Kudos [?]: 33 [1]
Given Kudos: 512
Send PM
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the [#permalink] New post   10 Mar 2023, 18:17
1
Kudos
Triangle ACE is similar to triangle BCD.
Attachments

File comment: Pfa
A871C650-05C1-430A-BD5A-ED4D167B2A06.jpeg
A871C650-05C1-430A-BD5A-ED4D167B2A06.jpeg [ 816.66 KiB | Viewed 858 times ]

GMAT Club Bot
gmatclubot
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the [#permalink]
10 Mar 2023, 18:17
Moderators:
Bunuel
Math Expert
92883 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions