If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 07 Dec 2016, 08:12

# Chicago-Booth

is Releasing R1 Admission Decisions | Keep Watch on App Tracker | Join Chat Room2 for Live Updates

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the

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

### Hide Tags

Manager
Joined: 28 Jun 2009
Posts: 52
Location: Moscow Russia
Schools: -=! LBS (int) !=- HEC (admitted) INSEAD (int)
Followers: 7

Kudos [?]: 14 [2] , given: 16

If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the [#permalink]

### Show Tags

03 Aug 2009, 22:09
2
This post received
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

77% (02:12) correct 23% (02:08) wrong based on 147 sessions

### HideShow timer Statistics

If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the area of trapezoid BEDC?

A. 12
B. 18
C. 24
D. 30
E. 48

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-be-cd-and-bc-ab-3-ae-4-and-cd-10-what-is-127060.html
Attachments

q.doc [68.5 KiB]
Downloaded 231 times

 To download please login or register as a user

Intern
Joined: 01 Aug 2009
Posts: 29
Location: Australia
Followers: 1

Kudos [?]: 17 [2] , given: 3

Re: Geo Q from ManhGmat. How to [#permalink]

### Show Tags

04 Aug 2009, 04:59
2
This post received
KUDOS
Answer: B (18)

Solution:
Since BE||CD, it implies that the triangle ABE and ACD are similar figures.

For triangle ABE,
AB=3
AE=4
BE =?

For triangle ACD,
AC=AB+BC = 3+3 = 6
AD = AE+ED = 4+?
CD =10

Since ABE and ACD are similar figures and AC = 2 AB (6=2*3), we can deduce the unknown sides, as the sides of ABE and ACD will follow the ratio of 1:2

For triangle ABE,
AB=3
AE=4
BE =(1/2)CD = (1/2)10 = 5

For triangle ACD,
AC=AB+BC = 3+3 = 6
AD = 2AE = 2*4 = 8
CD=10

Now that we know all sides, Area(BCDE) = Area(ACD) – Area(ABC)

Area of a triangle = sqrt(s(s-a)(s-b)(s-c)), where s=(a+b+c)/2 and abc are lengths of the sides.

Area(ACD) = sqrt(12*6*2*4) = 24
Area(ABC) = sqrt(6*3*2*1) = 6

Area(BCDE) = 24-6 = 18
_________________

The three most significant times in your life are:
1. When you fall in love
2. The birth of your first child
3. When you prepare for your GMAT

Director
Joined: 13 Nov 2003
Posts: 790
Location: BULGARIA
Followers: 1

Kudos [?]: 46 [4] , given: 0

Re: Geo Q from ManhGmat. How to [#permalink]

### Show Tags

04 Aug 2009, 05:36
4
This post received
KUDOS
Hi,

since BE is middle sector, parallel to the CD, E divides AD in two pieces of 4.
Triangle CDA is a right triangle with right angle at A , since sides are AC=6, CD=10 and AD=8.

Think that the solution is obvious. Area ACD=24, Area ABE=6 area of trapezoid is 18

regards
Intern
Joined: 06 Oct 2012
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Geo Q from ManhGmat. How to [#permalink]

### Show Tags

12 May 2013, 20:34
scarish wrote:
Answer: B (18)

Solution:
Since BE||CD, it implies that the triangle ABE and ACD are similar figures.

For triangle ABE,
AB=3
AE=4
BE =?

For triangle ACD,
AC=AB+BC = 3+3 = 6
AD = AE+ED = 4+?
CD =10

Since ABE and ACD are similar figures and AC = 2 AB (6=2*3), we can deduce the unknown sides, as the sides of ABE and ACD will follow the ratio of 1:2

For triangle ABE,
AB=3
AE=4
BE =(1/2)CD = (1/2)10 = 5

For triangle ACD,
AC=AB+BC = 3+3 = 6
AD = 2AE = 2*4 = 8
CD=10

Now that we know all sides, Area(BCDE) = Area(ACD) – Area(ABC)

Area of a triangle = sqrt(s(s-a)(s-b)(s-c)), where s=(a+b+c)/2 and abc are lengths of the sides.

Area(ACD) = sqrt(12*6*2*4) = 24
Area(ABC) = sqrt(6*3*2*1) = 6

Area(BCDE) = 24-6 = 18

please post a diagram of the aforesaid figure, it will help a lot, I simply can't just visualize it.
Intern
Joined: 05 Mar 2013
Posts: 45
Location: India
Concentration: Entrepreneurship, Marketing
GMAT Date: 06-05-2013
GPA: 3.2
Followers: 1

Kudos [?]: 49 [1] , given: 14

Re: If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the [#permalink]

### Show Tags

13 May 2013, 00:35
1
This post received
KUDOS
artuurss wrote:
If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the area of trapezoid BEDC?

A. 12
B. 18
C. 24
D. 30
E. 48

Be is parallel to cd so triangles ABE and ACD are similar. Ratio of their areas is square of the ratio of their similar sides.

Both the triangles are also similar so we can get ED as 4 which will indicate that ACD is a right angled triangle. so we can get the area as 24.and using ratio of areas statement stated above we can get the area of ABE as 6. So are of trapezoid is 24-6 = 18
_________________

"Kudos" will help me a lot!!!!!!Please donate some!!!

Completed
Official Quant Review
OG - Quant

In Progress
Official Verbal Review
OG 13th ed
MGMAT IR
AWA Structure

Yet to do
100 700+ SC questions
MR Verbal
MR Quant

Verbal is a ghost. Cant find head and tail of it.

Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90015 [5] , given: 10402

Re: If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the [#permalink]

### Show Tags

13 May 2013, 02:39
5
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED

If BE || CD, and BC = AB = 3, AE = 4 and CD = 10, what is the area of trapezoid BEDC?
A. 12
B. 18
C. 24
D. 30
E. 48

Triangles ABE and ACD are similar (they share the same angle CAD and also as BE is parallel to CD then angles by BE and CD are equal, so all 3 angles of these triangles are equal so they are similar triangles).

Property of similar triangles: ratio of corresponding sides are the same: $$\frac{AB}{AC}=\frac{BE}{CD}$$ --> $$\frac{3}{6}=\frac{BE}{10}$$ --> $$BE=5$$ and $$AD=2AE=8$$.

So in triangle ABE sides are $$AB=3$$, $$AE=4$$ and $$BE=5$$: we have 3-4-5 right triangle ABE (with right angle CAD, as hypotenuse is $$BE=5$$) and 6-8-10 right angle triangle ACD.

Now, the $$area_{BEDC}=area_{ACD}-area_{ABE}$$ --> $$area_{BEDC}=\frac{6*8}{2}-\frac{3*4}{2}=18$$.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-be-cd-and-bc-ab-3-ae-4-and-cd-10-what-is-127060.html

Also discussed here: trapezium-area-99966.html
_________________
Re: If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the   [#permalink] 13 May 2013, 02:39
Similar topics Replies Last post
Similar
Topics:
5 If (A+B) = 4, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)? 9 07 Jul 2016, 04:58
17 If AE=ED and AB=BC=CD, what is the value of x in the figure above? 2 10 May 2015, 03:39
52 If BE || CD, and BC = AB = 3, AE = 4 and CD = 10, what is 40 04 Feb 2012, 17:48
2 If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the 7 28 Aug 2010, 09:21
8 In the figure, AB = AE = 8, BC = CD = 13, and DE = 2. What is the area 4 08 Nov 2008, 17:58
Display posts from previous: Sort by

# If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.