document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258855>Question 258855</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a triangle has a hypotenuse of 50 <BR>\n" );
document.write( "the other sides of the triangle have the ratio of 16:9 <BR>\n" );
document.write( "what are the lengths of the sides 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 #190599 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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=190599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for the sides of a triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2+%2B+B%5E2+=+C%5E2 ALIGN=MIDDLE  ALT=\"A%5E2+%2B+B%5E2+=+C%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Where C is the hypotenuse.\r<BR>\n" );
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document.write( "In your case the two sides have a ratio to each other that is equal to 16:9 so we will modify the equation a little.\r<BR>\n" );
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document.write( "The new equation:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2AX%29%5E2+%2B+%289%2AX%29%5E2+=+C%5E2 ALIGN=MIDDLE  ALT=\"%2816%2AX%29%5E2+%2B+%289%2AX%29%5E2+=+C%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we know that C = 50<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2AX%29%5E2+%2B+%289%2AX%29%5E2+=+50%5E2 ALIGN=MIDDLE  ALT=\"%2816%2AX%29%5E2+%2B+%289%2AX%29%5E2+=+50%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can simplify this equation by squaring the terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256%2AX%5E2+%2B+81%2AX%5E2+=+2500 ALIGN=MIDDLE  ALT=\"256%2AX%5E2+%2B+81%2AX%5E2+=+2500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The left side can be rewritten by dividing X^2 out of it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+%2A+%28256+%2B+81%29+=+2500 ALIGN=MIDDLE  ALT=\"X%5E2+%2A+%28256+%2B+81%29+=+2500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+%2A+%28337%29+=+2500 ALIGN=MIDDLE  ALT=\"X%5E2+%2A+%28337%29+=+2500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 337<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+=+7.418 ALIGN=MIDDLE  ALT=\"X%5E2+=+7.418\"   DISABLED_style= \"max-width:90%; height:auto;\" > Note that from here on out I will be rounding so the numbers may not be exact<BR>\n" );
document.write( "Then take the square root of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+2.724 ALIGN=MIDDLE  ALT=\"X+=+2.724\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have to go back to the ratio that was given at the start of the problem<BR>\n" );
document.write( "16:9<BR>\n" );
document.write( "A = 16 * 2.724<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A+=+43.58%29 ALIGN=MIDDLE  ALT=\"highlight%28A+=+43.58%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B = 9 * 2.724<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28B+=+24.52%29 ALIGN=MIDDLE  ALT=\"highlight%28B+=+24.52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-----------<BR>\n" );
document.write( "Checking the answers<BR>\n" );
document.write( "Plug the calculated values back into the triagle equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2+%2B+B%5E2+=+C%5E2 ALIGN=MIDDLE  ALT=\"A%5E2+%2B+B%5E2+=+C%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43.58%5E2+%2B+24.52%5E2+=+50%5E2 ALIGN=MIDDLE  ALT=\"43.58%5E2+%2B+24.52%5E2+=+50%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1899.22+%2B+601.23+=+2500 ALIGN=MIDDLE  ALT=\"1899.22+%2B+601.23+=+2500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2500.45+=+2500 ALIGN=MIDDLE  ALT=\"2500.45+=+2500\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice the answer is off slightly due to rounding </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );