document.write( "Question 1014340: Find the perimeter of an equilateral triangle that can be inscribed in a circle whose circumference is 50 meters. \n" ); document.write( "

Algebra.Com's Answer #631265 by Fombitz(32388) $\"\"$ $\"About$

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So the radius of the circle is,
\n" ); document.write( " $\"2pi%2AR=50\"$
\n" ); document.write( " $\"R=25%2Fpi\"$
\n" ); document.write( "The equilateral triangle inscribed in the circle is made up of 3 isosceles triangles that have 2 sides equal to the radius of the circle and the third side equal to the length of the side of the equilateral triangle.
\n" ); document.write( "

.
\n" ); document.write( "From trigonometry,
\n" ); document.write( " $\"cos%2830%29=%28S%2F2%29%2FR\"$
\n" ); document.write( " $\"S=2Rcos%2830%29\"$
\n" ); document.write( "For an equlateral triangle,
\n" ); document.write( " $\"P=3S\"$
\n" ); document.write( " $\"P=6Rcos%2830%29\"$
\n" ); document.write( " $\"P=6%2825%2Fpi%29%28sqrt%283%29%2F2%29\"$
\n" ); document.write( " $\"P=%2875sqrt%283%29%29%2Fpi%29\"$
\n" ); document.write( " $\"highlight%28P=%2875sqrt%283%29%29%2Fpi%29%29\"$ \n" ); document.write( "

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