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# The bases of a certain prism are equilateral triangles, and the sides

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Math Expert
Joined: 02 Sep 2009
Posts: 54368
The bases of a certain prism are equilateral triangles, and the sides  [#permalink]

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08 Sep 2016, 04:24
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Difficulty:

35% (medium)

Question Stats:

73% (02:11) correct 27% (02:14) wrong based on 49 sessions

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The bases of a certain prism are equilateral triangles, and the sides of that prism are rectangles. If the area of each of the bases of the prism is 9√3 and the volume of the prism 18√3, then what is the area of one side of the prism?

A. 12
B. 12√3
C. 36
D. 36√3
E. 72

Attachment:

T6283.png [ 3.84 KiB | Viewed 1748 times ]

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Joined: 08 Jun 2013
Posts: 33
Re: The bases of a certain prism are equilateral triangles, and the sides  [#permalink]

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08 Sep 2016, 05:13
Area of equilateral triangle is √3/4a^2= 9√3
=> a^2 = 9×4 => a=6 which is base of rectangle
Vol of prism = area of triangle ×height
=> 18√3 = 9√3 × h
=> h = 2 which is length of rectangle
So, area of side = 6×2 =12

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Posts: 591
Re: The bases of a certain prism are equilateral triangles, and the sides  [#permalink]

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08 Sep 2016, 05:19
Bunuel wrote:

The bases of a certain prism are equilateral triangles, and the sides of that prism are rectangles. If the area of each of the bases of the prism is 9√3 and the volume of the prism 18√3, then what is the area of one side of the prism?

A. 12
B. 12√3
C. 36
D. 36√3
E. 72

Attachment:
T6283.png

Volume of triangular prism is v = b* h

we have base 9√3 and volume is 18√3

We get height as 18√3 = 9√3 * h => h = 2.

Equilateral triangle is √3 / 4* (a^2) = 9√3 ( since base is equilateral traingle)

a^2 = 36 => a = 6.

Now rectangle area is lb = 2*6 = 12.

IMO option A.
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Joined: 20 Jul 2016
Posts: 22
Re: The bases of a certain prism are equilateral triangles, and the sides  [#permalink]

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08 Sep 2016, 05:28
base of prism is an equilateral triangle:
Area = √3/4 * (Side)^2 = 9√3
so side = 6

Volume of this prism = Area of base * height
18√3 = 9√3 * height
So height = 2

Therefore Area of one side of prism = 2*6 = 12

Option A

Is this right?
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Location: United States (IL)
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Re: The bases of a certain prism are equilateral triangles, and the sides  [#permalink]

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09 Aug 2017, 15:25
applying properties of an equilateral triangle:
s^2 * sqrt(3) / 4 = 9 * sqrt(3)
that means that s=6.
knowing the volume, we can find the height, which is 2.
therefore, 6*2 = 12 - area of one side.
Re: The bases of a certain prism are equilateral triangles, and the sides   [#permalink] 09 Aug 2017, 15:25
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