Question

# A triangle with side lengths in the ratio 3 : 4 : 5 is inscribed in a circle of radius 3. The area of the triangle is equal to

A
8.64
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B
12
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C
6
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D
10.28
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Solution

## The correct option is A 8.64Le the lengths of the triangle be, 3x,4x,5xSquare of largest side = 25x2Sum of square of other sides = (3x)2+(4x)2=25x2Since, 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=65Now, two perpendicular sides are then, 185,245Area = 12×185×245 = 8.64

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