document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1004241>Question 1004241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The areas of two similar polygons are in the ratio 36:16. Find the ratio of the corresponding sides? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620770 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=620770\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the ratio of the sides will be equal to the square root of the ratio of the areas.\r<BR>\n" );
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document.write( "if the ratio of the areas is 36/16, then the ratio of the sides will be 6/4.\r<BR>\n" );
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document.write( "a couple of examples should confirm this.\r<BR>\n" );
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document.write( "assume a square.\r<BR>\n" );
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document.write( "s^2 = area.\r<BR>\n" );
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document.write( "let the large square have a side length of 6 and the small square have a side length of 4.\r<BR>\n" );
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document.write( "6^2 = 36<BR>\n" );
document.write( "4^2 = 16\r<BR>\n" );
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document.write( "assume a rectangle.\r<BR>\n" );
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document.write( "let the length and width of the large rectangle be equal to 12 and 6 and the small rectangle have a length of 8 and 4.\r<BR>\n" );
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document.write( "area of large rectangle = 12 * 6 = 72<BR>\n" );
document.write( "area of small rectangle = 8 * 4 = 32\r<BR>\n" );
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document.write( "ratio of area of large rectangle = 72/36 = 36/16.\r<BR>\n" );
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document.write( "the ratio of the sides is 6/4 and the ratio of the areas is 36/16.\r<BR>\n" );
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document.write( "6/4 is the square root of 36/16.\r<BR>\n" );
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document.write( "this applies to all polygons.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "assume an octagon (8 sides).\r<BR>\n" );
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document.write( "the area of the octagon is equal to 2 * (1 + sqrt(2)) * a^2\r<BR>\n" );
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document.write( "a is the side of the regular octagon.\r<BR>\n" );
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document.write( "it's clear that if a is 6, then the area will be equal to 36 * the constants, and that if a = 4, the area will be equal to 16 * the constants.\r<BR>\n" );
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document.write( "take the ratio of the larger area to the smaller area and it will becomes 36/16 because the constants, being the same value, will cancel out.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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