If the geometric mean of the lengths of three sides of a triangle is 3 and the area of the circumcir...........

Quantitative Aptitude ( CCS) Geometry

If the geometric mean of the lengths of three sides of a triangle is 3 and the area of the circumcircle is 9π, what is the area of the triangle (in sq. units)?

9/4

5/4

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Explanation:

Let the sides of the triangle be a, b, c and circumradius be R.
Geometric mean of a, b and c = (abc)^1/3 = 3
∴ abc = 3³ = 27
Area of circumcircle = πR² = 9π
∴ Circumradius = R = 3
Now, area of triangle = abc /4R = 9/4