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

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Math Expert
Joined: 02 Sep 2009
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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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07 Sep 2018, 00:22
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Difficulty:

15% (low)

Question Stats:

92% (00:48) correct 8% (00:48) wrong based on 30 sessions

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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 [ 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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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 $$area=\frac{(\sqrt[2]{3})}{4}*5^2$$
= $$\frac{25\sqrt{3}}{4}$$

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

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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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07 Sep 2018, 06:43
Bunuel wrote:

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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