Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 20 Jul 2019, 17:53

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.

Close

Request Expert Reply

Confirm Cancel

In the figure above AD = 4, AB = 3 and CD = 9

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Joined: 24 Aug 2012
Posts: 109
Reviews Badge
In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

Show Tags

New post 05 Mar 2014, 07:07
5
13
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

68% (02:55) correct 32% (03:02) wrong based on 266 sessions

HideShow timer Statistics


Image

In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?

A. 18
B. 13.5
C. 9
D. 4.5
E. 3

_________________
Push +1 kudos button please, if you like my post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56304
Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

Show Tags

New post 05 Mar 2014, 07:26
3
1
kingb wrote:
Image

In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?

A. 18
B. 13.5
C. 9
D. 4.5
E. 3


Attachment:
Untitled.png
Untitled.png [ 1.73 KiB | Viewed 32239 times ]

First of all notice that triangles CDE and BAE are similar (all three angles there are equal).

This means that the ratio of corresponding sides in these triangles are equal (corresponding sides are opposite equal angles): CD/AB = ED/AE --> 9/3 = ED/AE --> 3 = ED/AE --> 3*AE = ED.

Now, since AD = AE + ED = 4, then AE + 3*AE = 4 --> AE = 1 (and ED = 3).

The area of triangle AEC = 1/2*(base)*(height) = AE*CD = 1/2*1*9 = 4.5.

Answer: D.

Hope it's clear.
_________________
Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 542
Schools: Cambridge'16
Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

Show Tags

New post 05 Sep 2015, 00:50
Made guess that 2<ED<4 according to drawing, so ED=3

Area ACD=18, Area ECD=13.5. So, area AEC=18-13.5=4.5

D
Manager
Manager
avatar
Joined: 09 Aug 2015
Posts: 84
GMAT 1: 770 Q51 V44
GPA: 2.3
Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

Show Tags

New post 14 Sep 2015, 12:40
Area of triangle ABC = 6.

6 = 1/2 * b * h where the base is 3, and the height is 4.

Now notice that AEC is more than half of ABC, therefore 4.5 is the answer.
Manager
Manager
avatar
Joined: 06 Mar 2014
Posts: 89
Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

Show Tags

New post 11 Oct 2015, 06:17
1
Hi Bunuel:

Can you please explain how is the height CD for triangle AEC.
Why is the height of triangle AEC CD??
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56304
Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

Show Tags

New post 11 Oct 2015, 06:33
Shree9975 wrote:
Hi Bunuel:

Can you please explain how is the height CD for triangle AEC.
Why is the height of triangle AEC CD??


The altitude/height of a triangle is the perpendicular from the vertex to the opposite side. Note that the side may need to be extended. Thus CD is the height of AEC because CD is the perpendicular from vertex C to the line segment containing the opposite side AE.

Hope it's clear.
_________________
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2960
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

Show Tags

New post 21 Feb 2017, 22:49
1
kingb wrote:
Image

In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?

A. 18
B. 13.5
C. 9
D. 4.5
E. 3


Lay Down Foundation: Area of AEC = Area of ABC - Area of ABE

Also, Triangle ABE and CED are similar due to a pair of opposite angles and one right angle in each triangle

So AB/CD = AE/ED
i.e. 3/9 = AE/4-AE
i.e. AE = 1

So, Area of CED = [(1/2)*3*4 - (1/2)*3*1)] = 4.5

Answer: Option D
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Intern
avatar
B
Joined: 24 May 2016
Posts: 19
Location: Germany
Concentration: International Business, General Management
GMAT ToolKit User
Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

Show Tags

New post 08 May 2017, 08:44
Calculating the area for triangle ADC b*h/2 = 4*9/2= 18
From there you can eyeball and delete first of all option A. You see that triangle AEC is roughly one-third of triangle ADC, which would be 6.
The only option that comes close to that is option D.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11719
Re: In the figure above AD = 4, AB = 3 and CD = 9  [#permalink]

Show Tags

New post 02 Sep 2018, 09:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: In the figure above AD = 4, AB = 3 and CD = 9   [#permalink] 02 Sep 2018, 09:45
Display posts from previous: Sort by

In the figure above AD = 4, AB = 3 and CD = 9

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne