NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 12:12 It is currently 25 Apr 2024, 12:12
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

Point P is inside equilateral triangle ABC. Points Q, R, and S are the

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618998 [12]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Point P is inside equilateral triangle ABC. Points Q, R, and S are the [#permalink] New post   26 Mar 2019, 23:26
12
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

60% (02:45) correct 40% (02:36) wrong based on 80 sessions
Hide Show timer Statistics
Point P is inside equilateral triangle ABC. Points Q, R, and S are the feet of the perpendiculars from P to AB, BC, and CA, respectively. Given that PQ=1, PR=2, and PS=3, what is AB?

(A) 4
(B) \(3\sqrt{3}\)
(C) 6
(D) \(4\sqrt{3}\)
(E) 9
ShowHide Answer
Official Answer
D
avatar
B
itsanujsingh
Intern
Intern
Joined: 27 Sep 2018
Posts: 31
Own Kudos [?]: 36 [2]
Given Kudos: 14
Send PM
Re: Point P is inside equilateral triangle ABC. Points Q, R, and S are the [#permalink] New post   27 Mar 2019, 00:24
2
Kudos
Area of Triangle ABC= rt3/4 * a^2
where a = side of equailateral trianfle

Also, Area of Triangle ABC= Ar of traingle (PAB+PBC+PCA)
rt3/4 8a^2= 1/2*1*a+1/2*2*a+1/2*3*a
Solving we get a=4rt3
User avatar
D
rvgmat12
Senior Manager
Senior Manager
Joined: 19 Oct 2014
Posts: 394
Own Kudos [?]: 328 [1]
Given Kudos: 188
Location: United Arab Emirates
Schools: Wharton '23 Booth '23 INSEAD Jan'21 Intake
Send PM
GMAT ToolKit User Reviews Badge
Re: Point P is inside equilateral triangle ABC. Points Q, R, and S are the [#permalink] New post   24 Aug 2021, 02:42
1
Kudos
Root(3)/4*x^2 = 1/2(x+2x+3x)

x = 4root(3)
avatar
B
Harshjha001
Manager
Manager
Joined: 14 Sep 2019
Posts: 64
Own Kudos [?]: 24 [1]
Given Kudos: 19
Send PM
Re: Point P is inside equilateral triangle ABC. Points Q, R, and S are the [#permalink] New post   26 Aug 2021, 23:01
1
Bookmarks
D.

Sum of perpendiculars from a point to all the sides of an equilateral triangle is equal to the height of the equilateral triangle .

(1+2+3) = (root(3) / 2) *(side(s) of eq triangle).
side (s) = 4 * root(3)
User avatar
P
Crytiocanalyst
Director
Director
Joined: 16 Jun 2021
Posts: 994
Own Kudos [?]: 183 [0]
Given Kudos: 309
Send PM
Re: Point P is inside equilateral triangle ABC. Points Q, R, and S are the [#permalink] New post   27 Aug 2021, 06:52
Bunuel wrote:
Point P is inside equilateral triangle ABC. Points Q, R, and S are the feet of the perpendiculars from P to AB, BC, and CA, respectively. Given that PQ=1, PR=2, and PS=3, what is AB?

(A) 4
(B) \(3\sqrt{3}\)
(C) 6
(D) \(4\sqrt{3}\)
(E) 9


Key to solving the question is understanding the fact that the three triangles formed by the perpendiculars can be equalled to the area of the triangle

=1/2 *a (since all sides are equal ) * ( 1+2+3) = root3/ 4

=>1/2 *6*a = root 3/4

=>4*root3 =a

Therefore IMO D
avatar
D
TarunKumar1234
VP
VP
Joined: 14 Jul 2020
Posts: 1139
Own Kudos [?]: 1292 [0]
Given Kudos: 351
Location: India
Send PM
Re: Point P is inside equilateral triangle ABC. Points Q, R, and S are the [#permalink] New post   01 Sep 2021, 11:28
Sqrt(3)/4* a^2 = 1/2*a*(1+2+3)

or, a = 12/sqrt(3) = 4*sqrt(3)

So, I think D. :)
GMAT Club Bot
gmatclubot
Re: Point P is inside equilateral triangle ABC. Points Q, R, and S are the [#permalink]
01 Sep 2021, 11:28
Moderators:
Bunuel
Math Expert
92914 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