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# An equilateral triangle of area square centimeters is made out

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Joined: 02 Sep 2009
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13 Sep 2018, 04:57
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Difficulty:

35% (medium)

Question Stats:

82% (02:01) correct 18% (02:06) wrong based on 28 sessions

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An equilateral triangle of area $$25\sqrt{3}$$ square centimeters is made out of a piece of wire. What is the area of the largest circle that can be made by reshaping the same piece of wire?

A. $$\frac{25\pi}{\sqrt{3}}$$

B. $$\frac{225}{\pi}$$

C. 225

D. $$225\sqrt{3}$$

E. $$225\pi$$

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Re: An equilateral triangle of area square centimeters is made out  [#permalink]

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13 Sep 2018, 07:19
Imo B.

The area of the equilateral triangle can be found out using formula (√3/ 4 ) x (side of equilateral triangle)².
So here (√3/ 4 )*a^2=25√3.
a= 10. The perimeter of triangle is 30. This is the length of the wire.
So that would be the circumference of the circle so 30=2π ⋅ r
So r=15/π .
Area is π*r^2=225/π
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Re: An equilateral triangle of area square centimeters is made out  [#permalink]

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13 Sep 2018, 07:32
Bunuel wrote:
An equilateral triangle of area $$25\sqrt{3}$$ square centimeters is made out of a piece of wire. What is the area of the largest circle that can be made by reshaping the same piece of wire?

A. $$\frac{25\pi}{\sqrt{3}}$$

B. $$\frac{225}{\pi}$$

C. 225

D. $$225\sqrt{3}$$

E. $$225\pi$$

$$\frac{a^2√ 3}{4} = 25\sqrt{3}$$

So, $$a^2 = 100$$

Or, $$a = 10$$

Perimeter of the equilateral triangle $$= 30$$

Now, $$2πr = 30$$

Or, $$πr = 15$$

Or, $$r = 15/π$$

So, Area of the Circle must be $$πr^2 = π*\frac{15}{π}*\frac{15}{π}$$ = $$\frac{225}{\pi}$$, Answer must be (B)
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Re: An equilateral triangle of area square centimeters is made out   [#permalink] 13 Sep 2018, 07:32
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