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A circle is circumscribed about an equilateral triangle of side 'a'. The diameter of the circle is
(A) a v3 (where v3 denotes 'root-3')
(B) a / v3
(C) 2a/ v3
(D) 2 v(3a)
(E) 3 v(a)
HIGHLIGHT BELOW FOR OA:
Actual Answer : C
Explanation
Let R be the circumradius, then,
Area of the triangle = Product of sides of a triangle/4R.
Here, side of equilateral triangle = a. Area of equilateral triangle = 3^½/4 a². Therefore a * a * a/4R = (3^½/4)a². R = a/3^½. Diameter = 2R = 2a/3^½.
Hence (C) is the correct answer
This question is from Crack GMAT. I think the OA is incorrect. I approach this problem using trig as below
tan(30) = R/(a/2)
1/(3^1/2) = R/(a/2)
R = a/(2*(3^1/2))
=> Diameter = 2R = a/(3^1/2)
So the answer should be (B)
Tell me what you think.
(A) a v3 (where v3 denotes 'root-3')
(B) a / v3
(C) 2a/ v3
(D) 2 v(3a)
(E) 3 v(a)
HIGHLIGHT BELOW FOR OA:
Actual Answer : C
Explanation
Let R be the circumradius, then,
Area of the triangle = Product of sides of a triangle/4R.
Here, side of equilateral triangle = a. Area of equilateral triangle = 3^½/4 a². Therefore a * a * a/4R = (3^½/4)a². R = a/3^½. Diameter = 2R = 2a/3^½.
Hence (C) is the correct answer
This question is from Crack GMAT. I think the OA is incorrect. I approach this problem using trig as below
tan(30) = R/(a/2)
1/(3^1/2) = R/(a/2)
R = a/(2*(3^1/2))
=> Diameter = 2R = a/(3^1/2)
So the answer should be (B)
Tell me what you think.
--== Message from the GMAT Club Team ==--
THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
