document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=500319>Question 500319</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem:<BR>\n" );
document.write( "ABC is a right triangle. The length of its perimeter is equal to 60 units and the size of its area is equal to 150 units squared. Find the two sides and hypotenuse. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #338363 by </B><A HREF=/tutors/aboutme.mpl?userid=cleomenius><B>cleomenius(959)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=cleomenius><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=cleomenius><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=338363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Area f triangle = 150 = 1/2ab<BR>\n" );
document.write( "ab = 300<BR>\n" );
document.write( "a^2 + b^2 = c^2.<BR>\n" );
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document.write( "a + b + c = 60; the perimeter.<BR>\n" );
document.write( "a+ b = 60 - c rearrangement.<BR>\n" );
document.write( "square both sides.<BR>\n" );
document.write( "(a + b)^2 = (60 - c)^2<BR>\n" );
document.write( "a^2 + 2ab + b^2 = 3600 + c^2 - 120c<BR>\n" );
document.write( "subtract the equation A^2 + b^2 = c^2 (simultaneous equations)<BR>\n" );
document.write( "2ab = 3600 - 120c<BR>\n" );
document.write( "ab is known to be 300, hence<BR>\n" );
document.write( "600 = 3600 - 120c<BR>\n" );
document.write( "-3000 = -120c<BR>\n" );
document.write( "25 = c<BR>\n" );
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document.write( "substitute c by 25 in the equation a + b + c = 60  to obtain<BR>\n" );
document.write( "a + b + 25 = 60<BR>\n" );
document.write( "a + b = 35<BR>\n" );
document.write( "Since AB = 300 then b = 300/a which is substituted into the equation a + b = 35<BR>\n" );
document.write( "a + 300/a  - 35 = 0<BR>\n" );
document.write( "multiply all terms by a.<BR>\n" );
document.write( "a^2  -35a + 300 = 0<BR>\n" );
document.write( "Solve our quadratic equation.<BR>\n" );
document.write( "(x -15)(x - 20)<BR>\n" );
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document.write( "15, 20, 25 are our dimensions.<BR>\n" );
document.write( "15 + 20 + 25 = 60 units perimeter.<BR>\n" );
document.write( "This does check.<BR>\n" );
document.write( "15 * 20 = 300 units area.<BR>\n" );
document.write( "This does check.<BR>\n" );
document.write( "15^2 + 20^2 = 25^2 <BR>\n" );
document.write( "225 + 400 = 625 units.<BR>\n" );
document.write( "This does check also.<BR>\n" );
document.write( "Cleomenius<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );