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

It is currently 14 Dec 2019, 15:02

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

If side BE has length 10 and side AC has length 8, what is the area of

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59725
If side BE has length 10 and side AC has length 8, what is the area of  [#permalink]

Show Tags

New post 05 Nov 2019, 01:58
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (02:39) correct 37% (02:56) wrong based on 27 sessions

HideShow timer Statistics

Image
If side BE has length 10 and side AC has length 8, what is the area of the triangle BOC ?

A. \(2\sqrt{3}\)
B. \(4\sqrt{3}\)
C. \(6\sqrt{3}\)
D. \(8\sqrt{3}\)
E. \(12\sqrt{3}\)


Are You Up For the Challenge: 700 Level Questions


Attachment:
triangle BOC.JPG
triangle BOC.JPG [ 8.97 KiB | Viewed 470 times ]

_________________
Director
Director
User avatar
P
Joined: 16 Jan 2019
Posts: 507
Location: India
Concentration: General Management
WE: Sales (Other)
Re: If side BE has length 10 and side AC has length 8, what is the area of  [#permalink]

Show Tags

New post 05 Nov 2019, 05:19
1
\(ABC\) and \(BDE\) are both \(30-60-90\) right triangles and so their sides should be in the ratio \(1:\sqrt{3}:2\)

Therefore we have \(AC=8, BC=4, AB=4\sqrt{3}\) and \(BE=10, DE=5, BD=5\sqrt{3}\)

Draw \(OF\) perpendicular to \(BD\)

We now have 2 pairs of similar triangles

1. \(ABC\) & \(OFC\)
2. \(BDE\) & \(BOF\)

From \(ABC\) & \(OFC\)
\(\frac{OF}{FC}=\frac{4\sqrt{3}}{4}\) or \(OF=FC\sqrt{3}\)

From \(BDE\) & \(BOF\)
\(\frac{OF}{BF}=\frac{5}{5\sqrt{3}}\) or \(OF=\frac{BF}{\sqrt{3}}\)

So, \(FC\sqrt{3}=\frac{BF}{\sqrt{3}}\) or \(BF=3FC\)

We also know that \(BF+FC=BC=4\)
So, \(3FC+FC=4\) and \(FC=1\)

Therefore \(OF=\sqrt{3}\)

Area of \(BOC\)\(=\frac{1}{2}*BC*OF=\frac{1}{2}*4*\sqrt{3} = 2\sqrt{3}\)

Answer is (A)
VP
VP
User avatar
V
Joined: 19 Oct 2018
Posts: 1175
Location: India
Premium Member
Re: If side BE has length 10 and side AC has length 8, what is the area of  [#permalink]

Show Tags

New post 05 Nov 2019, 05:39
1
Triangle ACB is 30-60-90 triangle

AC=8
hence, BC=8/2=4

Triangle BOC is 30-60-90
Hence area of BOC= \(\frac{1}{2}*2*2\sqrt{3}\)= \(2\sqrt{3}\)


Bunuel wrote:
Image
If side BE has length 10 and side AC has length 8, what is the area of the triangle BOC ?

A. \(2\sqrt{3}\)
B. \(4\sqrt{3}\)
C. \(6\sqrt{3}\)
D. \(8\sqrt{3}\)
E. \(12\sqrt{3}\)


Are You Up For the Challenge: 700 Level Questions


Attachment:
The attachment triangle BOC.JPG is no longer available

Attachments

Untitled.png
Untitled.png [ 5.82 KiB | Viewed 354 times ]

Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)
Re: If side BE has length 10 and side AC has length 8, what is the area of  [#permalink]

Show Tags

New post 11 Nov 2019, 14:42
1
Bunuel wrote:
Image
If side BE has length 10 and side AC has length 8, what is the area of the triangle BOC ?

A. \(2\sqrt{3}\)
B. \(4\sqrt{3}\)
C. \(6\sqrt{3}\)
D. \(8\sqrt{3}\)
E. \(12\sqrt{3}\)


Are You Up For the Challenge: 700 Level Questions


Attachment:
triangle BOC.JPG


We see that triangle BOC is also a 30-60-90 right triangle, as are triangles ABC and BDE. That is because angle ABC is 60 degrees and angle EBD is 30 degrees, which means angle BOC must be 90 degrees.

Since AC = 8 and AC is the hypotenuse of triangle ABC, BC = 4, and AB = 4√3. Similarly, since BC = 4 and BC is the hypotenuse of triangle BOC, CO = 2, and BO = 2√3. Recall that the area of a right triangle is half the product of its legs; thus, the area of triangle BOC is:

1/2 x 2 x 2√3 = 2√3

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: If side BE has length 10 and side AC has length 8, what is the area of   [#permalink] 11 Nov 2019, 14:42
Display posts from previous: Sort by

If side BE has length 10 and side AC has length 8, what is the area of

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





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