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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] New post 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] New post 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] New post 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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Re: Equilateral Triangle Question [#permalink] New post 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.......
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Re: Equilateral Triangle Question [#permalink] New post 31 Dec 2011, 05:26
is there any other way solving the problem without using the area-formula for equilateral triangle?
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Re: Equilateral Triangle Question [#permalink] New post 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.
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Re: Equilateral Triangle Question [#permalink] New post 01 Jan 2012, 02:22
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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}

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Re: Equilateral Triangle Question [#permalink] New post 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] New post 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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If the area of an equilateral triangle is x square meters [#permalink] New post 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!

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If the area of an equilateral triangle is x square meters [#permalink] New post 26 Nov 2012, 15:37
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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 Image

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Re: If the area of an equilateral triangle is x square meters [#permalink] New post 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)
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Re: If the area of an equilateral triangle is x square meters [#permalink] New post 29 Jul 2013, 03:51
e is not equal to calculation is showing so come e is the answer. am i missing something...
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Re: If the area of an equilateral triangle is x square meters [#permalink] New post 29 Jul 2013, 04:52
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Re: If the area of an equilateral triangle is x square meters [#permalink] New post 29 Jul 2013, 05:39
Sorry Bunnel.... i see e is 4sqrt3.... Initially it seems to me like 4/3....please ignore my comment..
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Re: Equilateral Triangle Question [#permalink] New post 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 :cry:
Please help me out
Many thanks :wink:

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Re: Equilateral Triangle Question [#permalink] New post 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 :cry:
Please help me out
Many thanks :wink:


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! :-D
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Re: Equilateral Triangle Question [#permalink] New post 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 :cry:
Please help me out
Many thanks :wink:



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}

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Re: Equilateral Triangle Question   [#permalink] 16 Dec 2013, 19:23
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