document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207270>Question 1207270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the perimeter of an equilateral triangle whose area is equal to that of a triangle with sides 21 cm, 16 cm and 13 cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845047 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845047\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Triangle A = equilateral triangle<BR>\n" );
document.write( "Triangle B = triangle with sides 21, 16, and 13.\r<BR>\n" );
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document.write( "Let's apply Heron's Formula to find the area of triangle B.<BR>\n" );
document.write( "(a,b,c) = (21,16,13)<BR>\n" );
document.write( "s = semi-perimeter = half the perimeter<BR>\n" );
document.write( "s = (a+b+c)/2<BR>\n" );
document.write( "s = (21+16+13)/2<BR>\n" );
document.write( "s = 25<BR>\n" );
document.write( "area = sqrt(s*(s-a)*(s-b)*(s-c))<BR>\n" );
document.write( "area = sqrt(25*(25-21)*(25-16)*(25-13))<BR>\n" );
document.write( "area = sqrt(25*4*9*12)<BR>\n" );
document.write( "area = sqrt(10800)<BR>\n" );
document.write( "area = 103.9230485 square cm approximately\r<BR>\n" );
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document.write( "Now we use the area of an equilateral triangle formula so we can find the side length of triangle A.\r<BR>\n" );
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document.write( "x = side length<BR>\n" );
document.write( "area = 0.25*sqrt(3)*x^2<BR>\n" );
document.write( "sqrt(10800) = 0.25*sqrt(3)*x^2<BR>\n" );
document.write( "x^2 = 4*sqrt(10800)/sqrt(3)<BR>\n" );
document.write( "x^2 = 240<BR>\n" );
document.write( "x = sqrt(240)<BR>\n" );
document.write( "x = sqrt(16*15)<BR>\n" );
document.write( "x = sqrt(16)*sqrt(15)<BR>\n" );
document.write( "x = 4*sqrt(15)\r<BR>\n" );
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document.write( "Each side of triangle A is exactly 4*sqrt(15) cm long.<BR>\n" );
document.write( "Triple this to get the perimeter of the equilateral triangle.<BR>\n" );
document.write( "3*4*sqrt(15) = <font color=red>12*sqrt(15) cm</font>\r<BR>\n" );
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document.write( "12*sqrt(15) = 46.4758002 approximately<BR>\n" );
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