a triangle with side lengths in ratio 3:4:5 is inscribed in a circle of radius 3.find area of triang

Asked by  | 19th Apr, 2008, 10:57: PM

Expert Answer:

Since, the sides of the triangle are in the ratio 3:4:5, and 3,4 and 5 form a pythagorean triplet.

thus, we can conclude that the triangle is a right angled triangle.

we know that the circumcentre of a right triangle lies on its hypotenuse.

hence, the hypotenuse of the triangle forms the diameter of the circle.

radius of circle = 3

hence, hypotenuse of triangle = diameter = 6

i.e. 5x = 6 which implies x = 6/5 =1.2

hence, the other two sides are 3x = 3.6 and 4x = 4.8.

thus, the area of the triangle is 1/2 x base x height = 1/2 x 3.6 x 4.8 = 8.64 square units.

Answered by  | 10th Jul, 2008, 12:49: PM

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