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# If an equilateral triangle has an area of sqrt{243}, then what is the

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
If an equilateral triangle has an area of sqrt{243}, then what is the  [#permalink]

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05 Aug 2016, 04:18
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35% (medium)

Question Stats:

73% (01:33) correct 27% (02:02) wrong based on 230 sessions

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If an equilateral triangle has an area of $$\sqrt{243}$$, then what is the perimeter of that triangle?

A) 6

B) 12

C) 18

D) 27

E) 81

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If an equilateral triangle has an area of sqrt{243}, then what is the  [#permalink]

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05 Aug 2016, 05:42
Bunuel wrote:
If an equilateral triangle has an area of $$\sqrt{243}$$, then what is the perimeter of that triangle?

A) 6

B) 12

C) 18

D) 27

E) 81

Area of equailateral triangle is $$\sqrt{3}$$ * (a^2)/4 = $$\sqrt{243}$$

=> (a/2)^2 = $$\sqrt{243/3}$$
=> (a/2)^2 = $$\sqrt{81}$$
=> (a/2)^2 = 9
=> a/2 = 3 (only positive one)
=> a =6

Perimeter of equilateral triangle is 3a = 18.

IMO option C is correct answer..

OA please...will correct if I missed anything..
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Re: If an equilateral triangle has an area of sqrt{243}, then what is the  [#permalink]

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05 Aug 2016, 06:16
Top Contributor
Bunuel wrote:
If an equilateral triangle has an area of $$\sqrt{243}$$, then what is the perimeter of that triangle?

A) 6
B) 12
C) 18
D) 27
E) 81

Nice formula: Area of an equilateral triangle = (s²/4)(√3), where s = length of one side of triangle.
We're given the area, so we can write: (s²/4)(√3) = √243
Divide both sides by √3 to get: s²/4 = √81
Simplify right side to get: s²/4 = 9
Multiply both sides by 4 to get: s² = 36
Solve: s = 6

So, the PERIMETER = 6 + 6 + 6 = 18

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Re: If an equilateral triangle has an area of sqrt{243}, then what is the  [#permalink]

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11 Sep 2016, 10:18
I basically used the formula for area of an equilateral triangle:
(side)^2 * sqrt(3)/4
all this is equal to sqrt(243)
s^2 = sqrt(243)*4/sqrt(3)
let's get rid of sqrt(3), and multiply the new fraction by sqrt(3)/sqrt(3)
we get sqrt(729)*4/3 = 27*4/3 = 9*4 = 36
s^2 = 36
s=6
perimeter is 3s = 6*3 = 18.
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Re: If an equilateral triangle has an area of sqrt{243}, then what is the  [#permalink]

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03 Jul 2017, 05:21
Bunuel wrote:
If an equilateral triangle has an area of $$\sqrt{243}$$, then what is the perimeter of that triangle?

A) 6

B) 12

C) 18

D) 27

E) 81

Area of an equilateral triangle = $$\sqrt{3}$$/4 * a^2
$$\sqrt{3}$$/4 * a^2 = $$\sqrt{243}$$ =9$$\sqrt{3}$$
a^2 = 36
a = 6

So perimeter of equilateral triangle = 6*3 = 18

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Re: If an equilateral triangle has an area of sqrt{243}, then what is the  [#permalink]

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23 Sep 2018, 15:28
Bunuel wrote:
If an equilateral triangle has an area of $$\sqrt{243}$$, then what is the perimeter of that triangle?

A) 6

B) 12

C) 18

D) 27

E) 81

We can use the formula for the area of and equilateral triangle: area = (s^2√3)/4:

√243 = (s^2√3)/4

4√243 = s^2√3

4√81 = s^2

36 = s^2

6 = s

Since s = 6, the perimeter is 6 x 3 = 18.

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Re: If an equilateral triangle has an area of sqrt{243}, then what is the &nbs [#permalink] 23 Sep 2018, 15:28
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