Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50007

If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilatera
[#permalink]
Show Tags
25 Sep 2016, 09:50
Question Stats:
75% (01:55) correct 25% (02:13) wrong based on 139 sessions
HideShow timer Statistics



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3188
Location: India
GPA: 3.12

If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilatera
[#permalink]
Show Tags
25 Sep 2016, 17:22
The altitude of an equilateral triangle is \(side*\frac{√3}{2}\). As perimeter of triangle ACD is \(9+3√3\), AC + CD + AD = \((side+\frac{side}{2}+side*\frac{√3}{2}) = 9 + 3√3\) or side = 6. Perimeter of equilateral triangle, ABC is 3*side = 18(OptionC)
_________________
You've got what it takes, but it will take everything you've got



Intern
Joined: 02 Sep 2016
Posts: 21

If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilatera
[#permalink]
Show Tags
26 Sep 2016, 04:30
Bunuel wrote: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? We know that the angle bisector also bisects the opposite side in an equilateral triangle. Assume, AC=2a. This means AD=a (AB=2a, and C bisects AB). Also height is given by √3(side)/2 = √3a Perimeter = 2a+a+√3a=3a+√3a=9+3√3. from this, a=3, so side = 2a=6. Perimeter =18



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India

Re: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilatera
[#permalink]
Show Tags
26 Sep 2016, 05:25
Bunuel wrote: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? A. 9 B. 18−3√3 C. 18 D. 18+3√3 E. 27 Note the \(\sqrt{3}\) term. The perimeter will include the altitude AD which would probably be the \(3*\sqrt{3}\) term. Altitude of an equilateral triangle \(= \sqrt{3}*Side/2 = 3*\sqrt{3}\) Then Side is 6. If that is true, then the rest of the perimeter would be 6 + 3 (half of base) = 9 (which is correct) Perimeter of equilateral triangle ABC = 3*6 = 18
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 10 Jan 2014
Posts: 8

Re: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilatera
[#permalink]
Show Tags
26 Sep 2016, 06:17
Bunuel wrote: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? A. 9 B. 18−3√3 C. 18 D. 18+3√3 E. 27 Answer: In triangle ACD, angle ACD = 90; angle ACD = 60 (because equilateral triangle) So, <CAD = 30 Therefore sides AC = 2x CD=x & AD= \sqrt{3}x 2x+x+ 3\sqrt{3}x = 3+\sqrt{3}x So, x= 3 Hence, AC = 6 Perimeter = 6



Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 114
WE: Marketing (Consulting)

If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilatera
[#permalink]
Show Tags
27 Jan 2018, 03:21
Bunuel wrote: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? A. 9 B. 18−3√3 C. 18 D. 18+3√3 E. 27 I solved it in a different way, please let me know if I am taking any risks here: we know that the side opposite to angle 60 (altitude) = x √3 (1:√3:2) so if we consider "3√3" in ACD perimeter "9+ 3√3 " is the length of the altitude, then AC+ CD =9 Since this is equilateral triangle then the perimeter = 9*2=18 (C)
_________________
"it takes more time to fix a mistake than to avoid one" "Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything
High achievement always takes place in the framework of high expectation Charles Kettering If we chase perfection we can catch excellence Vince Lombardi
GMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmatclublive5principlesforfastmath251028.html#p1940045 YouTube sessions by GMATNinja: https://gmatclub.com/forum/verballivewithgmatninjascpronounsthatparallelism250568.html#p1936104 The Best SC strategies  Amazing 4 videos by Veritas: https://gmatclub.com/forum/thebestscstrategiesamazing4videosbyveritas250377.html#p1934575



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India

If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilatera
[#permalink]
Show Tags
29 Jan 2018, 05:36
NDND wrote: Bunuel wrote: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? A. 9 B. 18−3√3 C. 18 D. 18+3√3 E. 27 I solved it in a different way, please let me know if I am taking any risks here: we know that the side opposite to angle 60 (altitude) = x √3 (1:√3:2) so if we consider "3√3" in ACD perimeter "9+ 3√3 " is the length of the altitude, then AC+ CD =9 Since this is equilateral triangle then the perimeter = 9*2=18 (C) Yes, you can make that assumption but you do need to confirm once that \(CD:AD:AC = 1:\sqrt{3}:2\) If \(AD = 3\sqrt{3}\), then CD = 3 and AC = 6. They do add up to 9 and give perimeter as \(9 + 3\sqrt{3}\). All matches up. The reason you can't assume without confirming is what if the side x is \(\sqrt{3}\) and the side 2x is \(2\sqrt{3}\) and the \(\sqrt{3}x\) is then just 3?
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 114
WE: Marketing (Consulting)

Re: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilatera
[#permalink]
Show Tags
29 Jan 2018, 10:26
VeritasPrepKarishma wrote: NDND wrote: Bunuel wrote: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? A. 9 B. 18−3√3 C. 18 D. 18+3√3 E. 27 I solved it in a different way, please let me know if I am taking any risks here: we know that the side opposite to angle 60 (altitude) = x √3 (1:√3:2) so if we consider "3√3" in ACD perimeter "9+ 3√3 " is the length of the altitude, then AC+ CD =9 Since this is equilateral triangle then the perimeter = 9*2=18 (C) Yes, you can make that assumption but you do need to confirm once that \(CD:AD:AC = 1:\sqrt{3}:2\) If \(AD = 3\sqrt{3}\), then CD = 3 and AC = 6. They do add up to 9 and give perimeter as \(9 + 3\sqrt{3}\). All matches up. The reason you can't assume without confirming is what if the side x is \(\sqrt{3}\) and the side 2x is \(2\sqrt{3}\) and the \(\sqrt{3}x\) is then just 3? Thanks VeritasPrepKarishma So, is this applicable on this problem, how can we confirm here? do you advise not to use this way in this problem? Thx
_________________
"it takes more time to fix a mistake than to avoid one" "Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything
High achievement always takes place in the framework of high expectation Charles Kettering If we chase perfection we can catch excellence Vince Lombardi
GMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmatclublive5principlesforfastmath251028.html#p1940045 YouTube sessions by GMATNinja: https://gmatclub.com/forum/verballivewithgmatninjascpronounsthatparallelism250568.html#p1936104 The Best SC strategies  Amazing 4 videos by Veritas: https://gmatclub.com/forum/thebestscstrategiesamazing4videosbyveritas250377.html#p1934575



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India

Re: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilatera
[#permalink]
Show Tags
30 Jan 2018, 02:10
NDND wrote: So, is this applicable on this problem, how can we confirm here? do you advise not to use this way in this problem?
Thx
Here is how you can confirm here: The total perimeter is \(9 + 3\sqrt{3}\). If \(AD = 3\sqrt{3}\), then CD = 3 and AC = 6 to get the ratio \(1:\sqrt{3}:2\). CD and AC do add up to 9 and give perimeter as \(9 + 3\sqrt{3}\). All matches up.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3896
Location: United States (CA)

Re: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilatera
[#permalink]
Show Tags
31 Jan 2018, 17:06
Bunuel wrote: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? A. 9 B. 18−3√3 C. 18 D. 18+3√3 E. 27 Since triangle ABC is an equilateral triangle, angle ACD is 60 degrees. We also see that angle ADC is 90 degrees, so angle DAC is 30 degrees, and thus triangle ACD is a 306090 right triangle, with base CD = x, altitude AD = x√3, and hypotenuse AC = 2x. Thus: 3x + x√3 = 9 + 3√3 We see that x must be 3. So hypotenuse AC = side of triangle ABC = 2x = 2(3) = 6, and thus the perimeter of equilateral triangle ABC is 3 x 6 = 18. Answer: C
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilatera &nbs
[#permalink]
31 Jan 2018, 17:06






