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If the area of the circle shown above with center O is 25π, what is th

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If the area of the circle shown above with center O is 25π, what is th  [#permalink]

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New post 07 Sep 2018, 00:22
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If the area of the circle shown above with center O is 25π, what is the area of the equilateral triangle inside the circle?


A. 25/4

B. \(\frac{25\sqrt{3}}{4}\)

C. 25/2

D. \(\frac{25\sqrt{3}}{2}\)

E. \(25\sqrt{3}\)


Attachment:
image001.jpg
image001.jpg [ 1.95 KiB | Viewed 456 times ]

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Re: If the area of the circle shown above with center O is 25π, what is th  [#permalink]

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New post 07 Sep 2018, 02:50
Area of circle is\(\pi\)\(*r^2\)
\((\pi)*r^2= 25(\pi)\)
therefore, \(r=5\)

the equilateral triangle has 2 of its sides as radii
hence, side = \(r=5\)
there fore \(area=\frac{(\sqrt[2]{3})}{4}*5^2\)
= \(\frac{25\sqrt{3}}{4}\)

Answer: B
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Re: If the area of the circle shown above with center O is 25π, what is th  [#permalink]

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New post 07 Sep 2018, 03:09
Area of a equilateral triangle is root(3)/4 * a²


Hence answer b

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Re: If the area of the circle shown above with center O is 25π, what is th  [#permalink]

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New post 07 Sep 2018, 06:43
Bunuel wrote:
Image
If the area of the circle shown above with center O is 25π, what is the area of the equilateral triangle inside the circle?


A. 25/4

B. \(\frac{25\sqrt{3}}{4}\)

C. 25/2

D. \(\frac{25\sqrt{3}}{2}\)

E. \(25\sqrt{3}\)

Attachment:
image001.jpg

\(πr^2 = 25π\)

Or, \(r = 5\)

Thus, sides of the triangle are 5

Hence area of the equilateral triangle is \(\frac{25√3}{4}\) , ANswer must be (B)
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Re: If the area of the circle shown above with center O is 25π, what is th   [#permalink] 07 Sep 2018, 06:43
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