SOLUTION: A circle is inscribed in an equilateral triangle. If the circumference of the circle is 3.85 cm, calculate in cm, the perimeter of the triangle.

Question 717989: A circle is inscribed in an equilateral triangle. If the circumference of the circle is 3.85 cm, calculate in cm, the perimeter of the triangle.
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Realize, a 30-60-90 triangle is half of another equilateral triangle.

Use the circle's circumference to get it radius. The distance from the center of the circle to a midpoint of one of the sides of the triangle is a radius length and is one leg of a 30-60-90 triangle; the hypotenuse of this 30-60-90 triangle is TWICE the radius length.
Now, one half the length of the circumscribed equilateral triangle is the other leg of the 30-60-90 triangle. Use pythagorean theorem to find it and so if you multiply it by 2, you have the length of a side of the circumscribed equilateral triangle.

Back a little, you get radius r; you then have 2r, and 2r is hypotenuse of a 30 60 90 triangle. If y is hyptonuse for the 30 60 90 then . Find y.
6y is the perimeter you want.
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