document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160335>Question 1160335</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The areas of two similar triangles are 108 cm² and 972 cm². What is the ratio of the lengths of their 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 #783615 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=783615\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if tbhe triangles are similar, then their corresponding sides are proportional.\r<BR>\n" );
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document.write( "that means that the corresponding sides of one of the triangle is equal to x * the corresponding side of the other triangle.\r<BR>\n" );
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document.write( "the area of a triangle is equal to 1/2 * b * h<BR>\n" );
document.write( "b is one of the side.<BR>\n" );
document.write( "h is the other of the sides.\r<BR>\n" );
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document.write( "since the triangles are similar, then the sides of the second triangle would be x * the corresponding side.\r<BR>\n" );
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document.write( "therefore, the area of the first triangle is 1/2 * b * h and the area of the second triangle is 1/2  * x * b * x * h.<BR>\n" );
document.write( "this simplifies to 1/2 * x^2 * b * h.<BR>\n" );
document.write( "shown another way, it is equal to 1/2 * b * h * x^2.\r<BR>\n" );
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document.write( "if the area of the first triangle is 108 and the area of the second triangle is 972, then x^2 = 972 / 108 = 9\r<BR>\n" );
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document.write( "this makes x = 3.\r<BR>\n" );
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document.write( "the ratio of their corresponding sides is therefore 3.\r<BR>\n" );
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document.write( "to confirm, assume 1/2 * b * h = 108<BR>\n" );
document.write( "let b = 12 and h = 18<BR>\n" );
document.write( "you get 1/2 * b * h = 1/2 * 12 * 18 = 108.<BR>\n" );
document.write( "since x = 3, then the dimensions for the second triangle are:<BR>\n" );
document.write( "b = 3 * 12 = 36<BR>\n" );
document.write( "h = 3 * 18 = 54<BR>\n" );
document.write( "the area of the second triangle is equal to 1/2 * 36 * 54 = 972.\r<BR>\n" );
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document.write( "the ratio of the areas is 972 / 108 = 9<BR>\n" );
document.write( "the ratios of the corresponding sides is 3 which is the square root of the ratio of the area.\r<BR>\n" );
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document.write( "your solution is that the ratio of the area of the corresponding sides is the square root of the ratio of the areas which is the square root of 9 which is 3.\r<BR>\n" );
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