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If the area of an equilateral triangle is x square meters [#permalink]
29 Dec 2010, 17:25

00:00

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Difficulty:

25% (low)

Question Stats:

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?

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

Re: Equilateral Triangle Question [#permalink]
29 Dec 2010, 20:48

1

This post received 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

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.

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}

Re: Equilateral Triangle Question [#permalink]
02 Jan 2012, 03:28

1

This post received 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}

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)

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...

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

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.