If the area of an equilateral triangle is x square meters : GMAT Problem Solving (PS)
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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]

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29 Dec 2010, 17:25
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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
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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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29 Dec 2010, 20:48
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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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 25 Aug 2011 Posts: 22 Concentration: Entrepreneurship, General Management GMAT Date: 01-31-2012 Followers: 1 Kudos [?]: 2 [0], given: 56 Re: Equilateral Triangle Question [#permalink] ### Show Tags 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: 317 WE 1: IT 1 Yr WE 2: Supply Chain 5 Yrs Followers: 21 Kudos [?]: 252 [0], given: 11 Re: Equilateral Triangle Question [#permalink] ### Show Tags 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 [?]: 6 [0], given: 12 Re: Equilateral Triangle Question [#permalink] ### Show Tags 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: 7130 Location: Pune, India Followers: 2140 Kudos [?]: 13707 [0], given: 222 Re: Equilateral Triangle Question [#permalink] ### Show Tags 01 Jan 2012, 02:22 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 Get started with Veritas Prep GMAT On Demand for$199

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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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02 Jan 2012, 03:28
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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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Get started with Veritas Prep GMAT On Demand for $199 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] ### Show Tags 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 SVP Status: Yale SOM! Joined: 06 Feb 2012 Posts: 1552 Location: United States Concentration: Marketing, Strategy Followers: 51 Kudos [?]: 548 [1] , given: 345 If the area of an equilateral triangle is x square meters [#permalink] ### Show Tags 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 Note: I do not complete individual profile reviews. Please use the Admissions Consultant or Peer Review forums to get feedback on your profile. GMAT Club Premium Membership - big benefits and savings Intern Joined: 09 Jun 2012 Posts: 31 Followers: 0 Kudos [?]: 18 [0], given: 13 Re: If the area of an equilateral triangle is x square meters [#permalink] ### Show Tags 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) 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 [?]: 22 [0], given: 34 Re: Equilateral Triangle Question [#permalink] ### Show Tags 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: 472 Followers: 3 Kudos [?]: 160 [0], given: 134 Re: Equilateral Triangle Question [#permalink] ### Show Tags 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: 7130 Location: Pune, India Followers: 2140 Kudos [?]: 13707 [0], given: 222 Re: Equilateral Triangle Question [#permalink] ### Show Tags 16 Dec 2013, 19:23 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 Get started with Veritas Prep GMAT On Demand for$199

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Re: If the area of an equilateral triangle is x square meters [#permalink]

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25 Jul 2014, 02:42
VeritasPrepKarishma wrote:
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 = $$S/3 = 12*\sqrt{3}/3 = 4*\sqrt{3}$$

Hey Guys,

sorry to bring this topic up again. I got the right answer by being 80 % sure-guessing, but I couldn't calculate as you did.

Let's say side of triangle = a.

Then:
perimeter = x = 3a
area = x = $$a^2*\sqrt{3}/4$$

Hence

$$3a = a^2*\sqrt{3}/4 --> 3a/a^2 = \sqrt{3}/4 --> 3/a = \sqrt{3}/4$$

and so on. I don't see how I get to $$a = 4\sqrt{3}$$

Where is my error?

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27 Jul 2014, 19:19
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unceldolan wrote:
I got the right answer by being 80 % sure-guessing, but I couldn't calculate as you did.

Let's say side of triangle = a.

Then:
perimeter = x = 3a
area = x = $$a^2*\sqrt{3}/4$$

Hence

$$3a = a^2*\sqrt{3}/4 --> 3a/a^2 = \sqrt{3}/4 --> 3/a = \sqrt{3}/4$$

$$3/a = \sqrt{3}/4$$

Now cross multiply to get

$$3*4 = a*\sqrt{3}$$

$$\sqrt{3} * \sqrt{3} * 4 = a * \sqrt{3}$$

$$\sqrt{3} * 4 = a$$

So $$a = 4 * \sqrt{3}$$
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Current Student Joined: 21 Oct 2013 Posts: 194 Location: Germany GMAT 1: 660 Q45 V36 GPA: 3.51 Followers: 1 Kudos [?]: 37 [0], given: 19 Re: If the area of an equilateral triangle is x square meters [#permalink] ### Show Tags 27 Jul 2014, 20:47 VeritasPrepKarishma wrote: unceldolan wrote: I got the right answer by being 80 % sure-guessing, but I couldn't calculate as you did. Let's say side of triangle = a. Then: perimeter = x = 3a area = x = $$a^2*\sqrt{3}/4$$ Hence $$3a = a^2*\sqrt{3}/4 --> 3a/a^2 = \sqrt{3}/4 --> 3/a = \sqrt{3}/4$$ $$3/a = \sqrt{3}/4$$ Now cross multiply to get $$3*4 = a*\sqrt{3}$$ $$\sqrt{3} * \sqrt{3} * 4 = a * \sqrt{3}$$ $$\sqrt{3} * 4 = a$$ So $$a = 4 * \sqrt{3}$$ Ah okay, now I get this that's clever! Thank you! Current Student Status: GMAT Date: 10/08/15 Joined: 17 Jul 2014 Posts: 97 Location: United States (MA) Concentration: Human Resources, Strategy GMAT 1: 640 Q48 V35 GPA: 3.5 WE: Human Resources (Consumer Products) Followers: 0 Kudos [?]: 26 [0], given: 62 Re: If the area of an equilateral triangle is x square meters [#permalink] ### Show Tags 18 Apr 2015, 00:04 VeritasPrepKarishma wrote: unceldolan wrote: I got the right answer by being 80 % sure-guessing, but I couldn't calculate as you did. Let's say side of triangle = a. Then: perimeter = x = 3a area = x = $$a^2*\sqrt{3}/4$$ Hence $$3a = a^2*\sqrt{3}/4 --> 3a/a^2 = \sqrt{3}/4 --> 3/a = \sqrt{3}/4$$ $$3/a = \sqrt{3}/4$$ Now cross multiply to get $$3*4 = a*\sqrt{3}$$ $$\sqrt{3} * \sqrt{3} * 4 = a * \sqrt{3}$$ $$\sqrt{3} * 4 = a$$ So $$a = 4 * \sqrt{3}$$ Hi Karishma, Can you please tell me what am I doing wrong here: One side of traingle = x/3 Area = x x=√3/4 * (x/3)^2 x*(3/x)^2 =√3/4 9/x = √3/4 36=√3x 36/√3 =x Now if I rationalise - 36/√3 *√3/√3 --> I get 12*√3 Thanks, aimtoteach _________________ Thanks, aimtoteach ~~~~~~~~~~~~~~~~~ Please give Kudos if you find this post useful. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8339 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 382 Kudos [?]: 2473 [0], given: 164 Re: If the area of an equilateral triangle is x square meters [#permalink] ### Show Tags 18 Apr 2015, 10:52 Hi aimtoteach, Your math is fine, but you haven't answered the question that was ASKED. In your last 'step', you've figured out the value of X. The question asks for the length of ONE SIDE of the triangle; X is the PERIMETER of the equilateral triangle, so you have to divide this result by 3 to get the correct answer. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: If the area of an equilateral triangle is x square meters   [#permalink] 18 Apr 2015, 10:52

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