document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1077439>Question 1077439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A piece of metal has the shape of a right triangle. The hypotenuse is 3 ft shorter than four times the shortest side and the longer side is 10 ft longer than twice the shorter side. What is the length of the hypotenuse of the&#8203; triangle?<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 #691901 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=691901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> shorter side=x<BR>\n" );
document.write( "longer side is 2x+10<BR>\n" );
document.write( "hypotenuse is 4x-3<BR>\n" );
document.write( "square them all<BR>\n" );
document.write( "x^2+(2x+10)^=(4x-3)^2.  Note, binomial expansion (a+b)^2=a^2+2 ab (the internal products are doubled)+b^2<BR>\n" );
document.write( "x^4x^2+40x+100=16x^2-24x+9<BR>\n" );
document.write( "5x^2+40x+100=16x^2-24x+9<BR>\n" );
document.write( "0=11x^2-64x-91<BR>\n" );
document.write( "x=(1/22)(64+/- sqrt (4096+4004); sqrt 8100=90<BR>\n" );
document.write( "x=(1/22)(64+/-90), use only the + root.<BR>\n" );
document.write( "x=(1/22)154=7<BR>\n" );
document.write( "sides are 7, 24, with hypotenuse 25, a well known right triangle. </SPAN>\n" );
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