document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #440726 by josgarithmetic(39620) $\"\"$ $\"About$

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Realize, a 30-60-90 triangle is half of another equilateral triangle.\r
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\n" ); document.write( "\n" ); document.write( "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. \r
\n" ); document.write( "\n" ); document.write( "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. \r
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\n" ); document.write( "\n" ); document.write( "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 $\"y%5E2=r%5E2%2B%282r%29%5E2\"$ . Find y.
\n" ); document.write( "6y is the perimeter you want. \n" ); document.write( "

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