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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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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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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
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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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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: 0 Kudos [?]: 1 [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: 317 WE 1: IT 1 Yr WE 2: Supply Chain 5 Yrs Followers: 19 Kudos [?]: 169 [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 [?]: 2 [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: 5977 Location: Pune, India Followers: 1536 Kudos [?]: 8496 [0], given: 194 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 Get started with Veritas Prep GMAT On Demand for$199

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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
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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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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] 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: 1309 Location: United States Concentration: Marketing, Strategy Schools: Yale SOM - Class of 2015 Followers: 45 Kudos [?]: 466 [1] , given: 309 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 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 [?]: 11 [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) 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 [?]: 17 [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: 472 Followers: 1 Kudos [?]: 99 [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: 5977 Location: Pune, India Followers: 1536 Kudos [?]: 8496 [0], given: 194 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 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]  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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Re: If the area of an equilateral triangle is x square meters [#permalink]  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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Re: If the area of an equilateral triangle is x square meters [#permalink]  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!
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Re: If the area of an equilateral triangle is x square meters [#permalink]  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
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Re: If the area of an equilateral triangle is x square meters [#permalink]  18 Apr 2015, 10:52
Expert's post
Hi aimtoteach,

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.

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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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