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Question

A triangle with side lengths in the ratio 3:4:5 is inscribed in a circle of radius 3. What is the area of the triangle? Provide your answer as a decimal rounded to the nearest hundredth.

Accepted Answer

Let the sides of the triangle have lengths 3x, 4x, and 5x. The triangle is a right triangle, so its hypotenuse is a diameter of the circle. Thus 5x=2 3=6, so x=6/5. The area of the triangle is 12 3x 4x =12 185 245 =21625=8.64.