document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148845>Question 1148845</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of the longer leg of a right triangle is 19 inches more than five times the length of the shorter leg. The length of the hypotenuse is 20 inches more than five times the length of the shorter leg. Find the side lengths 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 #770176 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=770176\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a^2 + b^2 = c^2<BR>\n" );
document.write( "b is the shorter leg<BR>\n" );
document.write( "The length of the longer leg of a right triangle is 19 inches more than five times the length of the shorter leg.<BR>\n" );
document.write( "a = 5b + 19<BR>\n" );
document.write( " The length of the hypotenuse is 20 inches more than five times the length of the shorter leg.<BR>\n" );
document.write( "c = 5b + 20<BR>\n" );
document.write( " Find the side lengths of the triangle.<BR>\n" );
document.write( "(5b+19)^2 + b^2 = (5b+20)^2<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "25b^2 + 95b + 95b + 361 + b^2 = 25b^2 + 100b + 100b + 400<BR>\n" );
document.write( "25b^2 + 190b + 361 + b^2 = 25b^2 + 200b + 400<BR>\n" );
document.write( "combine on the left<BR>\n" );
document.write( "25b^2 - 25b^2 + b^2 + 190b - 200b + 361 - 400 = 0<BR>\n" );
document.write( "b^2 - 10b - 39  = 0<BR>\n" );
document.write( "factors to<BR>\n" );
document.write( "(b-13)(b+3) = 0<BR>\n" );
document.write( "Positive solution is all we want here<BR>\n" );
document.write( "b = 13<BR>\n" );
document.write( "then<BR>\n" );
document.write( "a = 5(13) + 19<BR>\n" );
document.write( "a = 84<BR>\n" );
document.write( "and<BR>\n" );
document.write( "c = 5(13) + 20<BR>\n" );
document.write( "c = 85<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check: <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2884%5E2+%2B+13%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2884%5E2+%2B+13%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 85<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );