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The area of the circle in the figure above is 25π . What is the perime

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The area of the circle in the figure above is 25π . What is the perime  [#permalink]

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New post 11 Sep 2018, 02:43
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72% (02:00) correct 28% (02:02) wrong based on 20 sessions

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The area of the circle in the figure above is 25π . What is the perime  [#permalink]

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New post 11 Sep 2018, 05:09
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Bunuel wrote:
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The area of the circle in the figure above is 25π . What is the perimeter of the inscribed equilateral triangle?


A. \(15\sqrt{3}\)

B. 15

C. \(7.5\sqrt{3}\)

D. 7.5

E. \(2.5\sqrt{3}\)


Attachment:
The attachment image008 (1).jpg is no longer available


Area pf the circle\(= πr^2 = 25π\)

i.e. \(r = 5\)

Join the vertices of triangle with centre of the circle so that equilateral triangle gets divided in three 120º-30º-30º triangles where 120º is teh angle drawn at the centre of the circle

Divide the 120º-30º-30º triangle into two 90º-30º-60º triangles which hahaev hypotenuse = 5
i.e. Side opposite to 30º = 5/2
and side opposite to 60º = 5√3/2 which is half of the length of the side of equilateral

i.e. side of equilateral triangle \(= 2*5√3/2 = 5√3\)
hence, Perimeter of the equilateral \(= 3*5√3 = 15√3\)


Answer: option A
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Re: The area of the circle in the figure above is 25π . What is the perime  [#permalink]

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New post 11 Sep 2018, 18:49
height of equi triangle is root3/2 side and median divides height in ratio 2:1 so 2/3*root3/2 side = 5( pi r^2 = pi*5^2)
so side = 5*3/root3
perimeter = 3 * side
5*3*root3*root3/root3 = 15*root3
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Re: The area of the circle in the figure above is 25π . What is the perime   [#permalink] 11 Sep 2018, 18:49
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