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# If the area of an equilateral triangle is x square meters

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If the area of an equilateral triangle is x square meters [#permalink]  29 Dec 2010, 17:25
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73% (02:12) correct 27% (02:30) wrong based on 153 sessions
If the area of an equilateral triangle is x square meters and the perimeter is x meters, then what is the length of one side of the triangle in meters?

A 6
B 8
C 4√2
D 2√3
E 4√3
[Reveal] Spoiler: OA
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Re: Equilateral Triangle Question [#permalink]  29 Dec 2010, 19:49
m990540 wrote:
Keep coming up with the wrong answer for this one! Any help would be greatly appreciated.

If the area of an equilateral triangle is x square meters and the perimeter is x meters, then what is the length of one side of the triangle in meters?

A 6
B 8
C 4√2
D 2√3
E 4√3

Let me try

Area of Equilateral triangle = perimeter
\sqrt{3/4}* S^2 = 3S

Simplifying the above equation would give E

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Re: Equilateral Triangle Question [#permalink]  29 Dec 2010, 20:48
1
KUDOS
Expert's post
m990540 wrote:
Keep coming up with the wrong answer for this one! Any help would be greatly appreciated.

If the area of an equilateral triangle is x square meters and the perimeter is x meters, then what is the length of one side of the triangle in meters?

A 6
B 8
C 4√2
D 2√3
E 4√3

If perimeter of equilateral triangle is x, its side must be x/3.
If side is x/3, its area must be (\sqrt{3}/4)*(x/3)^2[Area of equilateral triangle of side 'a' is (\sqrt{3}/4)*a^2]
Area of triangle = x = (\sqrt{3}/4)*(x/3)^2
3*(4/\sqrt{3}) = x/3
(4\sqrt{3}) = x/3 = side of the triangle

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Karishma
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Intern Joined: 25 Aug 2011 Posts: 22 Concentration: Entrepreneurship, General Management GMAT Date: 01-31-2012 Followers: 0 Kudos [?]: 0 [0], given: 56 Re: Equilateral Triangle Question [#permalink] 28 Dec 2011, 04:10 Hi, Can anyone simply ; (S^2*Square3)/4=3S (area of equilateral=perimeter) i can not get the correct answer....... Senior Manager Joined: 13 May 2011 Posts: 324 WE 1: IT 1 Yr WE 2: Supply Chain 5 Yrs Followers: 19 Kudos [?]: 118 [0], given: 11 Re: Equilateral Triangle Question [#permalink] 31 Dec 2011, 05:26 is there any other way solving the problem without using the area-formula for equilateral triangle? Intern Joined: 16 Dec 2011 Posts: 49 GMAT Date: 04-23-2012 Followers: 0 Kudos [?]: 0 [0], given: 12 Re: Equilateral Triangle Question [#permalink] 01 Jan 2012, 00:43 i think we cannot solve it without formula and if we know formula it will hardly take a minute to crack it........ appreciated if some one help us to solve it without formula. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4566 Location: Pune, India Followers: 1029 Kudos [?]: 4455 [0], given: 162 Re: Equilateral Triangle Question [#permalink] 01 Jan 2012, 02:22 Expert's post BDSunDevil wrote: is there any other way solving the problem without using the area-formula for equilateral triangle? If you don't know the equilateral triangle area formula, you will need to use the area formula for any triangle i.e. (1/2)*base*altitude You will get the area for the equilateral triangle. Since perimeter = x meters, length of side = x/3 meters. So base = x/3 What about the altitude? You need to use pythagorean theorem to figure it out. The altitude bisects the opposite side in an equilateral triangle so (x/3)^2 = (x/6)^2 + altitude^2 altitude =x/(2\sqrt{3}) Area of triangle = (1/2)*(x/3)*(x/(2\sqrt{3}) = x^2/12*\sqrt{3} This is the same as the formula (obviously!)\sqrt{3}/4 * (x/3)^2 = x^2/12*\sqrt{3} _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Intern
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Re: Equilateral Triangle Question [#permalink]  02 Jan 2012, 00:04
HI, can anyone explain how to get to the correct answer from here: (S^2*Square3)/4=3S.... I got S=12/square3
thanks!!
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Re: Equilateral Triangle Question [#permalink]  02 Jan 2012, 03:28
1
KUDOS
Expert's post
Saurajm wrote:
HI, can anyone explain how to get to the correct answer from here: (S^2*Square3)/4=3S.... I got S=12/square3
thanks!!

Length of the side = S/3 not S. S is the perimeter of the triangle (actually it is given as x in the original question)
So area =((S/3)^2*\sqrt{3})/4 = S
You get S = 12*\sqrt{3}
Length of side = S/3 = 12*\sqrt{3}/3 = 4*\sqrt{3}

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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Intern Joined: 26 Oct 2012 Posts: 10 GMAT 1: 690 Q45 V40 Followers: 1 Kudos [?]: 0 [0], given: 3 If the area of an equilateral triangle is x square meters [#permalink] 26 Nov 2012, 14:01 sorry to bring this up again, but can someone maybe explain to me how we go from (3*4)/rt3 to 4*rt3 ? I got 12/rt3 but I didn't know how to factor anymore then! Thanks a lot! Kate VP Status: Yale SOM! Joined: 06 Feb 2012 Posts: 1250 Location: United States Concentration: Marketing, Strategy Followers: 32 Kudos [?]: 409 [1] , given: 244 If the area of an equilateral triangle is x square meters [#permalink] 26 Nov 2012, 15:37 1 This post received KUDOS Expert's post KateG130290 wrote: sorry to bring this up again, but can someone maybe explain to me how we go from (3*4)/rt3 to 4*rt3 ? I got 12/rt3 but I didn't know how to factor anymore then! Thanks a lot! Kate (3*4)/rt3 = 12/rt3 = (12*rt3)/(rt3*rt3) = (12*rt3)/3 = 4*rt3 Posted from my mobile device _________________ aerien Get the best GMAT Prep Resources with GMAT Club Premium Membership Intern Joined: 09 Jun 2012 Posts: 31 Followers: 0 Kudos [?]: 6 [0], given: 13 Re: If the area of an equilateral triangle is x square meters [#permalink] 29 Jul 2013, 02:18 m990540 wrote: If the area of an equilateral triangle is x square meters and the perimeter is x meters, then what is the length of one side of the triangle in meters? A 6 B 8 C 4√2 D 2√3 E 4√3 Understanding the question: Questions talks about area, perimeter and side of an equilateral triangle. Facts to refer: Area of an equilateral triangle = (sqrt(3)/4)*a^2. As suggested by Karishma, if this formula is not known, then one can use the normal formula for area of triangle, (1/2 * bh), consider the 30-60-90 ratio and find the height. But knowing this formula can save valuable seconds. Perimeter of an equilateral triangle = 3a What's given in the question and what it implies (noted as =>): Area of an equilateral triangle = Perimeter => (sqrt(3)/4)*a^2 = 3a What is asked for: Value of a Solution: Solving (sqrt(3)/4)*a^2 = 3a => a = 4*sqrt(3) Manager Joined: 06 Jul 2013 Posts: 120 GMAT 1: 620 Q48 V28 GMAT 2: 700 Q50 V33 Followers: 0 Kudos [?]: 10 [0], given: 42 Re: If the area of an equilateral triangle is x square meters [#permalink] 29 Jul 2013, 03:51 e is not equal to calculation is showing so come e is the answer. am i missing something... Math Expert Joined: 02 Sep 2009 Posts: 18693 Followers: 3234 Kudos [?]: 22252 [0], given: 2602 Re: If the area of an equilateral triangle is x square meters [#permalink] 29 Jul 2013, 04:52 Expert's post AMITAGARWAL2 wrote: e is not equal to calculation is showing so come e is the answer. am i missing something... Can you please elaborate what you mean? _________________ Manager Joined: 06 Jul 2013 Posts: 120 GMAT 1: 620 Q48 V28 GMAT 2: 700 Q50 V33 Followers: 0 Kudos [?]: 10 [0], given: 42 Re: If the area of an equilateral triangle is x square meters [#permalink] 29 Jul 2013, 05:39 Sorry Bunnel.... i see e is 4sqrt3.... Initially it seems to me like 4/3....please ignore my comment.. Intern Joined: 11 Oct 2013 Posts: 18 Location: United Kingdom Concentration: General Management, Leadership GMAT 1: 490 Q32 V25 GPA: 3.9 WE: Other (Other) Followers: 0 Kudos [?]: 6 [0], given: 34 Re: Equilateral Triangle Question [#permalink] 16 Dec 2013, 18:14 VeritasPrepKarishma wrote: m990540 wrote: Keep coming up with the wrong answer for this one! Any help would be greatly appreciated. If the area of an equilateral triangle is x square meters and the perimeter is x meters, then what is the length of one side of the triangle in meters? A 6 B 8 C 4√2 D 2√3 E 4√3 If perimeter of equilateral triangle is x, its side must be x/3. If side is x/3, its area must be (\sqrt{3}/4)*(x/3)^2[Area of equilateral triangle of side 'a' is (\sqrt{3}/4)*a^2] Area of triangle = x = (\sqrt{3}/4)*(x/3)^2 3*(4/\sqrt{3}) = x/3 (4\sqrt{3}) = x/3 = side of the triangle Dear Karishma, I lost you way on step: (S/3)^2 * sqrt3/4=S After this step my simplifications I always get: S/3=12/sqrt3 here my calculation: (S/3)^2 * sqrt3/4=S---> S^2/9 * sqrt3/4=S---> S^2*sqrt3 / 36=S---> S^2*sqrt3 / S =36---> S* sqrt3=36---> S= 36/ sqrt3---> here we need to divide by 3 in order to find S/3---> s/3= 12/sqrt3 I understant that is just small silly mistake somewhere but I could not spot it Please help me out Many thanks _________________ Good things come to those who wait… greater things come to those who get off their ass and do anything to make it happen... Senior Manager Joined: 13 May 2013 Posts: 476 Followers: 1 Kudos [?]: 44 [0], given: 134 Re: Equilateral Triangle Question [#permalink] 16 Dec 2013, 18:20 3111987 wrote: VeritasPrepKarishma wrote: m990540 wrote: Keep coming up with the wrong answer for this one! Any help would be greatly appreciated. If the area of an equilateral triangle is x square meters and the perimeter is x meters, then what is the length of one side of the triangle in meters? A 6 B 8 C 4√2 D 2√3 E 4√3 If perimeter of equilateral triangle is x, its side must be x/3. If side is x/3, its area must be (\sqrt{3}/4)*(x/3)^2[Area of equilateral triangle of side 'a' is (\sqrt{3}/4)*a^2] Area of triangle = x = (\sqrt{3}/4)*(x/3)^2 3*(4/\sqrt{3}) = x/3 (4\sqrt{3}) = x/3 = side of the triangle Dear Karishma, I lost you way on step: (S/3)^2 * sqrt3/4=S After this step my simplifications I always get: S/3=12/sqrt3 here my calculation: (S/3)^2 * sqrt3/4=S---> S^2/9 * sqrt3/4=S---> S^2*sqrt3 / 36=S---> S^2*sqrt3 / S =36---> S* sqrt3=36---> S= 36/ sqrt3---> here we need to divide by 3 in order to find S/3---> s/3= 12/sqrt3 I understant that is just small silly mistake somewhere but I could not spot it Please help me out Many thanks Here is how I did it: We know that the side (S) = x and the area (A) = x^2 The area of an equilateral triangle = √(3) / 4 * s^2 So: √(3) / 4 * (S)^2 = (A) √(3) / 4 * (x)^2 = x^2 √3 * (x)^2 = 4*x^2 √3 = 4 4/√3 Hope this helps! Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4566 Location: Pune, India Followers: 1029 Kudos [?]: 4455 [0], given: 162 Re: Equilateral Triangle Question [#permalink] 16 Dec 2013, 19:23 Expert's post 3111987 wrote: VeritasPrepKarishma wrote: m990540 wrote: Keep coming up with the wrong answer for this one! Any help would be greatly appreciated. If the area of an equilateral triangle is x square meters and the perimeter is x meters, then what is the length of one side of the triangle in meters? A 6 B 8 C 4√2 D 2√3 E 4√3 If perimeter of equilateral triangle is x, its side must be x/3. If side is x/3, its area must be (\sqrt{3}/4)*(x/3)^2[Area of equilateral triangle of side 'a' is (\sqrt{3}/4)*a^2] Area of triangle = x = (\sqrt{3}/4)*(x/3)^2 3*(4/\sqrt{3}) = x/3 (4\sqrt{3}) = x/3 = side of the triangle Dear Karishma, I lost you way on step: (S/3)^2 * sqrt3/4=S After this step my simplifications I always get: S/3=12/sqrt3 here my calculation: (S/3)^2 * sqrt3/4=S---> S^2/9 * sqrt3/4=S---> S^2*sqrt3 / 36=S---> S^2*sqrt3 / S =36---> S* sqrt3=36---> S= 36/ sqrt3---> here we need to divide by 3 in order to find S/3---> s/3= 12/sqrt3 I understant that is just small silly mistake somewhere but I could not spot it Please help me out Many thanks Your solution is correct. NOte that I get : x/3 = (4\sqrt{3}) = side of the triangle You get S/3=12/\sqrt{3} They are the same. You just need to further simplify to rationalize the denominator. 12/\sqrt{3} = 4*3/\sqrt{3} = 4*\sqrt{3}*\sqrt{3}/\sqrt{3} = 4*\sqrt{3} _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: Equilateral Triangle Question   [#permalink] 16 Dec 2013, 19:23
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