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

Saurajm

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Re: Equilateral Triangle Question [#permalink]

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.......

BDSunDevil

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Re: Equilateral Triangle Question [#permalink]

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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Re: Equilateral Triangle Question [#permalink]

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.

L

KarishmaB

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Re: Equilateral Triangle Question [#permalink]

01 Jan 2012, 03:22

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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]

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!!

L

KarishmaB

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Re: Equilateral Triangle Question [#permalink]

02 Jan 2012, 04:28

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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]

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]

26 Nov 2012, 16:37

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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

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

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

What is asked for:
Value of a

Solution:
Solving (sqrt(3)/4)*a^2 = 3a => a = 4*sqrt(3)

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Re: Equilateral Triangle Question [#permalink]

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 :cry:

Please help me out
Many thanks :wink:

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Re: Equilateral Triangle Question [#permalink]

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 :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

L

KarishmaB

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Re: Equilateral Triangle Question [#permalink]

16 Dec 2013, 20:23

Expert Reply

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

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?

thanks for your help!

L

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

27 Jul 2014, 20:19

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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, 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]

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

L

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

18 Apr 2015, 11:52

GMAT Problem Solving (PS) Questions

If the area of an equilateral triangle is x square meters