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geometry tough questn

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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geometry tough questn

by sukh » Tue Aug 23, 2011 8:10 am
ABCDEFGH is a cube. If the length of the diagonals DF, AG & CE are equal to sides of a triangle , then the circumradius of that triangle would be
a)equal to sides of the cube
b)under-root 3 times the sides of the cube
c) 1/ under-root 3 times the side of the cube
d) Indeterminate
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by amit.phatak » Tue Aug 23, 2011 12:20 pm
I think it is equal to side of the cube
Ans : A

Explanation :
lets say Side of the cube = a
diagonal = sqrt(3) * a
for equilateral triangle (with sides = DF, AG & CE) each side = sqrt(3) * a
circumradius of equilateral triangle = 2/3 * sqrt(3)/2 * side = 2/3 * sqrt(3)/2 * sqrt(3) * a

Therefore, circumradius = a = side of the cube.
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by Brent@GMATPrepNow » Wed Aug 24, 2011 9:51 am
sukh wrote:ABCDEFGH is a cube. If the length of the diagonals DF, AG & CE are equal to sides of a triangle , then the circumradius of that triangle would be
a)equal to sides of the cube
b)under-root 3 times the sides of the cube
c) 1/ under-root 3 times the side of the cube
d) Indeterminate
Amit is correct - the answer is A.

Aside: I should point out that, on the GMAT, you are not required to know the definition of "circumradius."

The question is also somewhat confusing to follow, and the 4 answer choices indicate that it is not a true GMAT question.

I mention all of this so that students do not become overly concerned if they didn't get the correct answer.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Abhishek009 » Sun Aug 28, 2011 9:56 am
sukh wrote:ABCDEFGH is a cube. If the length of the diagonals DF, AG & CE are equal to sides of a triangle , then the circumradius of that triangle would be
a)equal to sides of the cube
b)under-root 3 times the sides of the cube
c) 1/ under-root 3 times the side of the cube
d) Indeterminate
Length of the diagonals of a cube is : √3 * a

Sides of the triangle are equal ( Derived from the following statement - diagonals DF, AG & CE are equal to sides of a triangle )

Now Sides of a triangle is √3 * a

We know circumradius of an equilateral triangle is : (√3/3)* sides of an equilateral triangle.


So circumradius of the triangle is :

(√3/3) * √3 * a => a


So option a follows !!
Abhishek
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