document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=411412>Question 411412</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you find the area of a right triangle if you only know the length of the hypotenuse (6)and the perimeter (14) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #289193 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=289193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how do you find the area of a right triangle if you only know the length of the hypotenuse (6)and the perimeter (14)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Area = base*height <BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Perimeter = base + height + hypotenuse = 14<BR>\n" );
document.write( "b + h +6 = 14<BR>\n" );
document.write( "b + h = 8<BR>\n" );
document.write( "b = 8-h<BR>\n" );
document.write( "b^2 = (8-h)^2<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Using Pythagoras:<BR>\n" );
document.write( "b^2 + h^2 = 6^2<BR>\n" );
document.write( "b^2 = 36-h^2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve for \"b\":<BR>\n" );
document.write( "(8-h)^2 = 36- h^2<BR>\n" );
document.write( "64-16h+h^2 = 36-h^2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2h^2-16h+28 = 0<BR>\n" );
document.write( "h^2-8h+14 = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "h = [8 +- sqrt(64-4*14)]/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "h = [8 +- sqrt(8)]/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "h = 4+sqrt(2)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Solve for \"b\":<BR>\n" );
document.write( "b^2 = 36-h^2<BR>\n" );
document.write( "h^2 = (4+sqrt(2))^2 = 16+8sqrt(2)+2 = 18+8sqrt(2)<BR>\n" );
document.write( "b^2 = 36-(18+8sqrt(2)<BR>\n" );
document.write( "b^2 = 18-8sqrt(2)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Area = (1/2)bh<BR>\n" );
document.write( "Area = (1/2)(sqrt[18-8sqrt(2)])[4+sqrt(2)]<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=========<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );