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

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Bunuel
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If an equilateral triangle has an area of sqrt{243}, then what is the [#permalink] New post   05 Aug 2016, 05:18
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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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C
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BrentGMATPrepNow
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If an equilateral triangle has an area of sqrt{243}, then what is the [#permalink] New post   Updated on: 08 Feb 2021, 09:13
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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

Answer: C

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Originally posted by BrentGMATPrepNow on 05 Aug 2016, 07:16.
Last edited by BrentGMATPrepNow on 08 Feb 2021, 09:13, edited 1 time in total.
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If an equilateral triangle has an area of sqrt{243}, then what is the [#permalink] New post   05 Aug 2016, 06:42
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] New post   11 Sep 2016, 11:18
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] New post   03 Jul 2017, 06:21
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

Answer C
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Re: If an equilateral triangle has an area of sqrt{243}, then what is the [#permalink] New post   23 Sep 2018, 16:28
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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.

Answer: C
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Re: If an equilateral triangle has an area of sqrt{243}, then what is the [#permalink] New post   22 Nov 2021, 22:36
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Area of a equilateral triangle = \(\frac{\sqrt{3}}{4} * a^2\)

\(\frac{\sqrt{3}}{4} * a^2\) =\( \sqrt{243} \)= \(9\sqrt{3}\)

\(a^2\) = 9*4 = 36
a = 6.

Perimeter of a triangle = 3*a = 3*6 = 18

Option C is the answer.

Thanks,
Clifin J Francis,
GMAT SME
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Re: If an equilateral triangle has an area of sqrt{243}, then what is the [#permalink] New post   03 Apr 2024, 03:27
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Re: If an equilateral triangle has an area of sqrt{243}, then what is the [#permalink]
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