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The bases of a certain prism are equilateral triangles, and

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The bases of a certain prism are equilateral triangles, and

by swerve » Mon Oct 28, 2019 9:57 am
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The bases of a certain prism are equilateral triangles and the side of that prism are rectangles. If the area of each of the bases of the prism is \(9\sqrt{3}\) and the volume of the prism \(18\sqrt{3}\), then what is the area of the one side of the prism?

A. \(12\)
B. \(12\sqrt{3}\)
C. \(36\)
D. \(36\sqrt{3}\)
E. \(72\)

The OA is A

Source: Economist GMAT
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by joao_cardoso123 » Sun Nov 10, 2019 9:59 am
since the area of the base is 9*sqrt(3) and the volume is 18*sqrt(3) we know that the height (h) of the prism is 2

the area of a triangle is base*height/2

since it is a equilateral triangle, we can choose any side to be the base (b), and the height (a) of the triangle can be calculated from the equation
(b/2)^2+a^2=b^2

which gives a=(sqrt(3)*b)/2

replacing "a" in the equation of the area of the triangle and making it equal to 9*sqrt(3) gives us:
9*sqrt(3)=b*b*sqrt(3)/(2*2)
which shows that b=6

b*h=12
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