document.write( "Question 563793: The larger circle circumscribes an equilateral triangle, which circumscribes a small circle. The area of the larger circle is 12pi. What is the triangle's perimeter. I not sure how to do this problem and how to work it out. \n" ); document.write( "

Algebra.Com's Answer #852273 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "The larger circle circumscribes an equilateral triangle, which circumscribes a small circle.
\n" ); document.write( "The area of the larger circle is 12pi. What is the triangle's perimeter.
\n" ); document.write( "I not sure how to do this problem and how to work it ou
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\n" ); document.write( "\n" ); document.write( "In this problem, the smaller circle is irrelevant, so we can omit any mention about it.
\n" ); document.write( "Therefore, I will reformulate the problem by removing everything that does not matter:\r
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document.write( "    The circle circumscribes an equilateral triangle. The area of the circle is 12pi. \r\n" );
document.write( "    What is the triangle's perimeter ?\r\n" );
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\n" ); document.write( "\n" ); document.write( "Below is the solution for this modified formulation.\r
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document.write( "For any triangle with the side lengths 'a', 'b' and 'c', the radius of the circumscribed circle is\r\n" );
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document.write( "    R = ,     (1)\r\n" );
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document.write( "where A is the area of the triangle.  In our case, all three sides are congruent a = b = c,\r\n" );
document.write( "so the radius of the circumscribed circle is \r\n" );
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document.write( "    R = .     (2)\r\n" );
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document.write( "The area of the circumscribed circle is  A =  square units.\r\n" );
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document.write( "Substituting it into the formula (1), we get\r\n" );
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document.write( "    R =  = .    (3)\r\n" );
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document.write( "We are given that  the area of the circle is , so we can write this equation\r\n" );
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document.write( "     = .\r\n" );
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document.write( "Cancel    in both sides to get\r\n" );
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document.write( "     = 12.\r\n" );
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document.write( "Substitute here R from (3).  You will get\r\n" );
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document.write( "     = 12.\r\n" );
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document.write( "Simplify and find 'a'\r\n" );
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document.write( "     = 3*12 = 36,   a =  = 6 units.\r\n" );
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document.write( "Hence, the perimeter of the triangle is 3*6 = 18 units.\r\n" );
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document.write( "ANSWER.  The perimeter of the triangle is 18 units.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus we produced short, straightforward, compact and elegant Geometry solution.\r
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