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# If an equilateral triangle has an area equal to, what is its perimeter

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Math Expert
Joined: 02 Sep 2009
Posts: 50572
If an equilateral triangle has an area equal to, what is its perimeter  [#permalink]

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09 Sep 2018, 08:01
00:00

Difficulty:

15% (low)

Question Stats:

85% (00:38) correct 15% (01:40) wrong based on 27 sessions

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If an equilateral triangle has an area equal to $$a\sqrt{3}$$, what is its perimeter, in terms of a?

A. $$\sqrt{a}$$

B. $$2\sqrt{a}$$

C. $$6\sqrt{a}$$

D. 2a

E. 6a

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CEO
Joined: 11 Sep 2015
Posts: 3113
Re: If an equilateral triangle has an area equal to, what is its perimeter  [#permalink]

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09 Sep 2018, 08:11
Top Contributor
Bunuel wrote:
If an equilateral triangle has an area equal to $$a\sqrt{3}$$, what is its perimeter, in terms of a?

A. $$\sqrt{a}$$

B. $$2\sqrt{a}$$

C. $$6\sqrt{a}$$

D. 2a

E. 6a

Useful formula:
Area of an equilateral triangle = (side²)(√3/4)
We're told the area = a√3

So, we can write: (side²)(√3/4) = a√3
Divide both sides by √3 to get: (side²)/4 = a
Multiply both sides by 4 to get: side² = 4a
Take square root of both sides to get: side = √(4a) = (√4)(√a) = 2√a

So, ONE side of the equilateral triangle has length 2√a

So, the PERIMETER = 2√a + 2√a + 2√a = 6√a

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com

Re: If an equilateral triangle has an area equal to, what is its perimeter &nbs [#permalink] 09 Sep 2018, 08:11
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