document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108259>Question 1108259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a right triangle is 144 cm. The base is 12 cm. less than the width. Find the area. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723287 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=723287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = width<BR>\n" );
document.write( "x-12 = base<BR>\n" );
document.write( "c= hypotenuse <BR>\n" );
document.write( "Perimeter = x + x-12 + c = 144<BR>\n" );
document.write( "2x+c -12 = 144<BR>\n" );
document.write( "2x+c= 156<BR>\n" );
document.write( "c=156-2x\r<BR>\n" );
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document.write( "\n" );
document.write( "Since it's a right triangle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28x-12%29%5E2+=+%28156-2x%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28x-12%29%5E2+=+%28156-2x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+x%5E2-24x+%2B+144+=+156%5E2+-+624x+%2B+4x%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+x%5E2-24x+%2B+144+=+156%5E2+-+624x+%2B+4x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-24x+%2B144=+24336+-624x%2B4x%5E2 ALIGN=MIDDLE  ALT=\"2x%5E2+-24x+%2B144=+24336+-624x%2B4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+2x%5E2-600x+%2B+24192 ALIGN=MIDDLE  ALT=\"0=+2x%5E2-600x+%2B+24192\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+x%5E2+-300x+%2B+12096 ALIGN=MIDDLE  ALT=\"0=+x%5E2+-300x+%2B+12096\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Rewrite this to solve by completing the square \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-300+%2B+____=-12096+%2B+______ ALIGN=MIDDLE  ALT=\"x%5E2+-300+%2B+____=-12096+%2B+______\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+300+%2B+22500+=+-12096+%2B+22500 ALIGN=MIDDLE  ALT=\"x%5E2+-+300+%2B+22500+=+-12096+%2B+22500\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-150%29+%5E2+=+10404 ALIGN=MIDDLE  ALT=\"+%28x-150%29+%5E2+=+10404\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Take square root of both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-150=0+%2B-102 ALIGN=MIDDLE  ALT=\"x-150=0+%2B-102\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=150+%2B-102 ALIGN=MIDDLE  ALT=\"x=150+%2B-102\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=252 ALIGN=MIDDLE  ALT=\"x=252\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=48 ALIGN=MIDDLE  ALT=\"x=48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first answer is an extraneous root and must be rejected since the perimeter exceeds 144.  The second answer gives legs of a right triangle to be 48 and 36, so the area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+1%2F2+%2A48%2A36+=+864+cm%5E2 ALIGN=MIDDLE  ALT=\"A=+1%2F2+%2A48%2A36+=+864+cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >   \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Dr. Robert J. Rapalje, Retired<BR>\n" );
document.write( "Email:  rapaljer@mathinlivingcolor.com\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For more FREE help with math, please see my website at www.mathinlivingcolor.com<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );