GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 24 May 2019, 13:10

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, if BD = 6, what is the area of ∆ ABE?

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55271
In the figure above, if BD = 6, what is the area of ∆ ABE?  [#permalink]

Show Tags

New post 08 Aug 2017, 10:37
1
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (02:25) correct 42% (02:19) wrong based on 33 sessions

HideShow timer Statistics

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2759
Re: In the figure above, if BD = 6, what is the area of ∆ ABE?  [#permalink]

Show Tags

New post 08 Aug 2017, 14:05
Bunuel wrote:
Image
In the figure above, if BD = 6, what is the area of ∆ ABE?

(A) 8
(B) 10
(C) 12
(D) 14
(E) 16

Attachment:
The attachment 2017-08-08_2136.png is no longer available

Attachment:
trapezoidabcd_2136.png
trapezoidabcd_2136.png [ 35.05 KiB | Viewed 938 times ]

I think Answer A.

To find area of ∆ABE, use (area of trapezoid) - (area of blue ∆ ADE + area of yellow ∆ BCD)

1. Area of trapezoid

Polygon ABCD is a trapezoid: two right angles mean that side BC is parallel to side AD

BD = height of trapezoid = 6

ABCD area = \(\frac{(8 + 4)}{2}\) * 6 = 36

2. Area of two colored triangles - start with similar triangles to find height of blue ∆ ADE

Use properties of similar triangles to find height of blue triangle ADE

∆ ADE (blue) and ∆ BCE (light yellow) are similar:

Both have right angles. Their vertical angles are equal. AA = AAA. And the other two angles marked in red are alternate interior angles of parallel lines cut by transversal segment AC.

Corresponding sides of similar triangles will be in the same ratio.

Base AD of blue triangle is 8. Corresponding base BC of light yellow triangle is 4. Ratio is 2:1

Use the ratio to find height, DE, of blue triangle ADE.

Height of light yellow triangle BCE is BE

\(\frac{DE}{BE} = \frac{2x}{1x}\)

BD = 6

BD = sum of the heights of both similar triangles, i.e. BD = DE + BE

6 = 2x + x
x = 2

So BE is 2, and DE (height of blue triangle) is 4. See figure.

3. Find area of the two colored triangles (blue ∆ ADE and two-toned yellow ∆ BCD)

Area of blue ∆ ADE = \(\frac{b*h}{2}\) = \(\frac{4*8}{2}\)= 16

Area of two-toned yellow triangle BCD = \(\frac{4*6}{2}\) = 12

Total area of both colored triangles is 16 + 12 = 28

Area of trapezoid = 36

36 - 28 = 8

Area of ∆ ABE = 8

Answer A, IMO
_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.
Current Student
User avatar
P
Joined: 18 Aug 2016
Posts: 618
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Reviews Badge
Re: In the figure above, if BD = 6, what is the area of ∆ ABE?  [#permalink]

Show Tags

New post 08 Aug 2017, 21:08
1
Bunuel wrote:
Image
In the figure above, if BD = 6, what is the area of ∆ ABE?

(A) 8
(B) 10
(C) 12
(D) 14
(E) 16

Attachment:
2017-08-08_2136.png


Area of ∆ BCD = 12
Area of ∆ ABD = 24

From figure ∆ BCE & ∆ AED
BC:AD = 4:8 => BE:ED = 2:4

Area of ∆ AED =16 => Area of ∆ ABE = Area of ∆ ABD - Area of ∆ AED = 24 - 16 =8

A
_________________
We must try to achieve the best within us


Thanks
Luckisnoexcuse
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
In the figure above, if BD = 6, what is the area of ∆ ABE?  [#permalink]

Show Tags

New post 08 Aug 2017, 21:29
3
Image

Area of ∆ABD = \(\frac{1}{2}*AD*BD = \frac{1}{2}*6*8 = 24\)

From figure,
Angle B = Angle D
Angle E is common in both the triangles(opposite angles)
Therefore by AA similarity, ∆BCE is similar to ∆AED.

We know that the relative sides are proportional in similar triangle.
Hence,
\(\frac{BC}{AD} = \frac{BE}{ED}\)

\(\frac{4}{8} = \frac{BE}{ED}\)

\(ED = 2BE\) but we also know that \(BE + ED = 6\)

Therefore, \(BE = 2\) and \(ED = 4\)

Area of triangle ∆AED : \(\frac{1}{2}*AE*ED = \frac{1}{2}*8*4 = 16\)

Since we need the area of ∆ABE, it must be area of ∆ABD - area of ∆AED
Thus, Area of ∆ABE = 24 - 16 = 8(Option A)
_________________
You've got what it takes, but it will take everything you've got
GMAT Club Bot
In the figure above, if BD = 6, what is the area of ∆ ABE?   [#permalink] 08 Aug 2017, 21:29
Display posts from previous: Sort by

In the figure above, if BD = 6, what is the area of ∆ ABE?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

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®.