document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=390664>Question 390664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi. if my hypotenuse is 600, and the perimeter of the entire triangle is 1400, how long is the two other sides?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #278089 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=278089\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From the Pythagorean theorem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+=+360000 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+=+360000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "From the perimeter condition, x + y + 600 = 1400, or y = 800 - x.<BR>\n" );
document.write( "Substitute this into the 1st equation, to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28800+-+x%29%5E2+=+360000 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28800+-+x%29%5E2+=+360000\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-+1600x+%2B+280000+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+-+1600x+%2B+280000+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+800x+%2B+140000+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+800x+%2B+140000+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Using the quadratic formula, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28800+%2B-+200sqrt%282%29%29%2F2+=+400+%2B-+100sqrt%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28800+%2B-+200sqrt%282%29%29%2F2+=+400+%2B-+100sqrt%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+400+%2B+100sqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+400+%2B+100sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+400+-+100sqrt%282%29 ALIGN=MIDDLE  ALT=\"y+=+400+-+100sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+400+-+100sqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+400+-+100sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+400+%2B+100sqrt%282%29 ALIGN=MIDDLE  ALT=\"y+=+400+%2B+100sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Hence there is only 1 pair of values for the legs, and those are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+400+-+100sqrt%282%29 ALIGN=MIDDLE  ALT=\"+400+-+100sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400+%2B+100sqrt%282%29 ALIGN=MIDDLE  ALT=\"400+%2B+100sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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