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# What is the perimeter of an equilateral triangle inscribed

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Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
The radius of circum circle of an equilateral triangle = a/sqrt(3). a is the side of triangle.
Here: a/sqrt(3) = 4
a = 4*sqrt(3).
perimeter 3a = 3*4*sqrt(3) = 12sqrt(3).
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
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arthuro69 wrote:
What is the perimeter of an equilateral triangle inscribed in a circle of radius 4 ?

A. $$6\sqrt{2}$$
B. $$6\sqrt{3}$$
C. $$12\sqrt{2}$$
D. $$12\sqrt{3}$$
E. $$24$$

All you need to know about triangles for the GMAT: math-triangles-87197.html

Hope it helps.
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
Let x be the side of triangle.

Using cosine rule:
(x/2)/R = cos 30
=> x = 2Rcos 30 = 4√3
=> Perimeter = 3X = 12√3
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
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arthuro69 wrote:
What is the perimeter of an equilateral triangle inscribed in a circle of radius 4 ?

A. $$6\sqrt{2}$$
B. $$6\sqrt{3}$$
C. $$12\sqrt{2}$$
D. $$12\sqrt{3}$$
E. $$24$$

way simpler to simply know a formula :

Whenever a Circle circumscribes an equilateral triangle, the The radius of the circle can be defined by : Radius = $$\frac{Side Of The Triangle}{\sqrt{3}}$$.

that way, if we solve the problem : 4 = $$\frac{s}{\sqrt{3}}$$ . Hence, side = $$4\sqrt{3}$$.

Now, the perimeter = 3 x $$4\sqrt{3}$$ = 12$$\sqrt{3}$$ .
The answer is the option D.
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
For equilateral triangle the radius of the circumscribed circle R = Side * $$Root 3/3$$
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
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