document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=465192>Question 465192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ratio of the areas of two similar triangles is 4:5. If the legs of the smaller triangle are 3cm and 4cm, how long is the hypotenuse of the larger triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318818 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of the smaller triangle is 5.\r<BR>\n" );
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document.write( "To find the hypotenuse of the larger triangle, note that the areas are in the ratio 4:5, with 4 corresponding to the smaller triangle. This is a two dimensional specification, so if we take the square root we will obtain the ratio of side lengths (one dimensional).\r<BR>\n" );
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document.write( "The ratio of the side lengths of the two triangles is 2:sqrt(5). Here we can build a ratio:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2}{\sqrt{5}} = \frac{5 cm}{x cm}\">\r<BR>\n" );
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document.write( "Solving, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = \frac{5\sqrt{5}}{2}\">. </SPAN>\n" );
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