The correct option is A 8.64
Le the lengths of the triangle be, 3x,4x,5x
Square of largest side = 25x2
Sum of square of other sides = (3x)2+(4x)2=25x2
Since, the square of largest side is equal to the sum of square of other sides, hence, it is a right angled triangle.
For a right angled triangle the diameter of the circumcircle is equal to the hypotenuse of the triangle.
hence, 5x=6 or x=65
Now, two perpendicular sides are then, 185,245
Area = 12×185×245 = 8.64