document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262938>Question 262938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.  If the perimeter of a rectangle is 26 meters, and the area is 30 square meters,<BR>\n" );
document.write( "what is the diagonal?\r<BR>\n" );
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document.write( "2.  A right triangle has area 30 square meters and perimeter 30 meters. What is<BR>\n" );
document.write( "its hypotenuse?\r<BR>\n" );
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document.write( "I understand how to do #1 (via quadratic equation), but I don't see how to set-up #2, with the triangle perimeter info.  The solution must be under my nose, but I just don't see it (as of yet).\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193704 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=193704\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the perimeter of a rectangle is 26 meters, and the area is 30 square meters,<BR>\n" );
document.write( "what is the diagonal?\r<BR>\n" );
document.write( "\n" );
document.write( "2.  A right triangle has area 30 square meters and perimeter 30 meters. What is<BR>\n" );
document.write( "its hypotenuse?\r<BR>\n" );
document.write( "\n" );
document.write( "I understand how to do #1 (via quadratic equation), but I don't see how to set-up #2, with the triangle perimeter info.  The solution must be under my nose, but I just don't see it (as of yet).\r<BR>\n" );
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document.write( "Thank you.\r<BR>\n" );
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document.write( "1. Perimeter of triangle = 2*(l+w)\r<BR>\n" );
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document.write( "26=  2*(l+w)<BR>\n" );
document.write( "13= l+w<BR>\n" );
document.write( "LB =30\r<BR>\n" );
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document.write( "Let length be x<BR>\n" );
document.write( "Width = 13-x\r<BR>\n" );
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document.write( "X*(13-x)= 30\r<BR>\n" );
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document.write( "13x-x^2=30\r<BR>\n" );
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document.write( "X^2-13x+30=0\r<BR>\n" );
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document.write( "X^2-10x-3x+30=0<BR>\n" );
document.write( "X(x-10)-3(x-10)=0<BR>\n" );
document.write( "(x-10)(x-3) =0\r<BR>\n" );
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document.write( "X=3 or 10  The length and breadth can be said to be 10 and 3  meters\r<BR>\n" );
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document.write( "2.  Area of right triangle =30 square meters<BR>\n" );
document.write( "     <BR>\n" );
document.write( "•a + b + h = 30  a  and b  are the sides and h the hypo\r<BR>\n" );
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document.write( "(1 / 2) a b = 30   or    a b = 60 \r<BR>\n" );
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document.write( "a 2 + b 2 = h 2 <BR>\n" );
document.write( "•Rewrite the equation a + b + h = 60 as follows \r<BR>\n" );
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document.write( "a + b = 30 - h <BR>\n" );
document.write( "•Square both sides \r<BR>\n" );
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document.write( "(a + b)2 = (30 - h)2 <BR>\n" );
document.write( "•Expand both sides \r<BR>\n" );
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document.write( "a2 + b2 + 2 a b = 302 + h2 - 60 h <BR>\n" );
document.write( "•Combine the equation a 2 + b 2 = h 2 with the above equation to obtain \r<BR>\n" );
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document.write( "2 a b = 302 - 60 h <BR>\n" );
document.write( "•a b is known to be equal to 60, hence the above equation becomes \r<BR>\n" );
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document.write( "120 = 302 - 60 h <BR>\n" );
document.write( "•Solve for h to obtain \r<BR>\n" );
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document.write( "h = 13 units <BR>\n" );
document.write( "•Substitute h by 13 in the equation a + b + h = 60 to obtain \r<BR>\n" );
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document.write( "a + b +13=30  =17<BR>\n" );
document.write( "•Since a b = 60, then b = 60 / a which is substituted in the equation a + b = 60 to obtain \r<BR>\n" );
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document.write( "a + 60 / a - 17 = 0 <BR>\n" );
document.write( "•Multiply all terms by a to obtain a quadratic equation of the form \r<BR>\n" );
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document.write( "a 2 + 60 - 17 a = 0 <BR>\n" );
document.write( "•Solve the above equation to obtain two solutions <BR>\n" );
document.write( "a^2-17a+60=0<BR>\n" );
document.write( "Use the equation a b = 60 to obtain \r<BR>\n" );
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document.write( "when a 12 , b = 5 and when a = 5 , b =12 <BR>\n" );
document.write( "•The two sides of the right triangle and the hypotenuse are, respectively, given by \r<BR>\n" );
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document.write( "5 units, 12 units and 13 units. \r<BR>\n" );
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document.write( "mananth@hotmail.com<BR>\n" );
document.write( " </SPAN>\n" );
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