document.write( "Question 429889: Find the side length of a equilateral triangle with an area of 12 radical 3. \n" ); document.write( "

Algebra.Com's Answer #298586 by Gogonati(855) $\"\"$ $\"About$

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Solution:Let x cm the side of equilateral triangle, then half of its perimeter will be: 3x/2 cm. If we apply Heron's Formula of triangle area, we have:\r
\n" ); document.write( "\n" ); document.write( " $\"A=sqrt%28%28p-a%29%2A%28p-b%29%2A%28p-c%29%29\"$ , where p is half of perimeter and a=b=c=x cm the \r
\n" ); document.write( "\n" ); document.write( "sides of triangle.Substitute the given of our problem:\r
\n" ); document.write( "\n" ); document.write( " $\"12sqrt%283%29=sqrt%28%28%283x%2F2%29-x%29%29%5E3\"$ , squaring both sides,\r
\n" ); document.write( "\n" ); document.write( " $\"432=%28%283x%2F2%29-x%29%5E3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"432=x%5E3%2F8\"$ ,\r
\n" ); document.write( "\n" ); document.write( "x^3=432(8) => x=cubic root((432)(8)) => x=12(cubic root(2))cm\r
\n" ); document.write( "\n" ); document.write( "Done. \n" ); document.write( "

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