document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=903536>Question 903536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sides of certain right triangles are Pythagorean triples, the sum of one of the sides of the triangle plus the hypotenuse equals 49 cm. Find the sum, in cm, of the lengths of the this sides of all triangles that satisfy this criteria.\r<BR>\n" );
document.write( "\n" );
document.write( "A) 63<BR>\n" );
document.write( "B) 56<BR>\n" );
document.write( "C) 28<BR>\n" );
document.write( "D) 72<BR>\n" );
document.write( "E) 65 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #548265 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=548265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sides of certain right triangles are Pythagorean triples, the sum of one of the sides of the triangle plus the hypotenuse equals 49 cm.<BR>\n" );
document.write( "a + c = 49<BR>\n" );
document.write( "c = (49-a)<BR>\n" );
document.write( "Phythag: a^2 + b^2 = c^2<BR>\n" );
document.write( "replace c <BR>\n" );
document.write( "a^2 + b^2 = (49-a)^2<BR>\n" );
document.write( "a2 + b^2 = 2401 - 98a + a^2<BR>\n" );
document.write( "subtract a^2 from both sides<BR>\n" );
document.write( "b^2 = 2401 - 98a<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282401-98a%29 ALIGN=MIDDLE  ALT=\"sqrt%282401-98a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using the graphing feature on a Ti83. x=a; y=b<BR>\n" );
document.write( "enter<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282401-98x%29 ALIGN=MIDDLE  ALT=\"sqrt%282401-98x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using the table found only 3 integer solutions<BR>\n" );
document.write( "x=12; y=35<BR>\n" );
document.write( "x=20; y=21<BR>\n" );
document.write( "x=24; y=7<BR>\n" );
document.write( "Corresponds to triples of (subtract x from 49 to find c<BR>\n" );
document.write( "a=12; b=35; c=37; sum: 84<BR>\n" );
document.write( "a=20; b=21; c=29; sum: 70<BR>\n" );
document.write( "a=24; b=7;  c=25; sum: 56\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );