document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=239329>Question 239329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of each side of an isosceles triangle is a prime number. The perimeter of the triangle is greater than 21 units and is not a prime number. What is the least possible perimeter of the triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175728 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=175728\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The perimeter of an isosceles triangle is equal to 2*s + b where s equals one of the equal sides of the triangle and b equals the base.\r<BR>\n" );
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document.write( "If the base is equal to one of the sides, then you have an equilateral triangle.\r<BR>\n" );
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document.write( "The perimeter of this triangle has to be greater than 21 units and is not a prime number.\r<BR>\n" );
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document.write( "Possible perimeters are therefore:\r<BR>\n" );
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document.write( "22,23,24,25,26,27,28,29,30,...\r<BR>\n" );
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document.write( "The length of each side of the triangle has to be a prime number.   \r<BR>\n" );
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document.write( "I presume this includes the base of the triangle as well as the 2 equal sides.\r<BR>\n" );
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document.write( "Since 7*3 = 21, one of the sides of this triangle has to be greater than 7 at least.\r<BR>\n" );
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document.write( "We'll start with the next highest prime number which is 11.\r<BR>\n" );
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document.write( "If 11 is the base of the triangle, then the smallest side could be 7 which would make the total perimeter equal to 14 + 11 = 25.\r<BR>\n" );
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document.write( "25 is not a prime.\r<BR>\n" );
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document.write( "25 looks good.\r<BR>\n" );
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document.write( "If 11 was a side of the triangle, then the perimeter of the triangle could be 22 + 2 = 24\r<BR>\n" );
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document.write( "24 is not a prime.\r<BR>\n" );
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document.write( "24 looks good.\r<BR>\n" );
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document.write( "None of the other combinations produce a perimeter less than 24.\r<BR>\n" );
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document.write( "23 would be no good because it's a prime number.\r<BR>\n" );
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document.write( "The smallest possible perimeter that meets the requirements is 22 but no combinations I was able to find yielded a total of 22.\r<BR>\n" );
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document.write( "I'd go with 24 which is a combination of 2 times 11 plus 2.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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