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

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Intern
Joined: 19 Dec 2010
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If the area of an equilateral triangle is x square meters [#permalink]

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29 Dec 2010, 18:25
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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, 20:49
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, 21:48
1
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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28 Dec 2011, 05:10
Hi,
Can anyone simply ;
(S^2*Square3)/4=3S (area of equilateral=perimeter)
i can not get the correct answer.......
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31 Dec 2011, 06:26
is there any other way solving the problem without using the area-formula for equilateral triangle?
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01 Jan 2012, 01:43
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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01 Jan 2012, 03:22
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!)$$\sqrt{3}/4 * (x/3)^2 = x^2/12*\sqrt{3}$$
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02 Jan 2012, 01:04
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, 04:28
1
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]

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26 Nov 2012, 15:01
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
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If the area of an equilateral triangle is x square meters [#permalink]

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26 Nov 2012, 16:37
1
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
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Re: If the area of an equilateral triangle is x square meters [#permalink]

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29 Jul 2013, 03:18
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

Value of a

Solution:
Solving (sqrt(3)/4)*a^2 = 3a => a = 4*sqrt(3)
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16 Dec 2013, 19:14
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
Many thanks
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16 Dec 2013, 19:20
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
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!
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16 Dec 2013, 20:23
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
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.

$$12/\sqrt{3} = 4*3/\sqrt{3} = 4*\sqrt{3}*\sqrt{3}/\sqrt{3} = 4*\sqrt{3}$$
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Re: If the area of an equilateral triangle is x square meters [#permalink]

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25 Jul 2014, 03:42
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]

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27 Jul 2014, 20:19
1
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]

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27 Jul 2014, 21:47
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]

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18 Apr 2015, 01:04
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]

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18 Apr 2015, 11:52
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, 11:52

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