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

Question

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

msk0657 · Answer

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..

BrentGMATPrepNow · Answer

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

RELATED VIDEO
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mvictor · Answer

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.

shashankism · Answer

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

ScottTargetTestPrep · Answer

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

CrackverbalGMAT · Answer

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

bumpbot · Answer

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

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

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