document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148002>Question 148002</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The longer leg of a right triangle is 1cm longer than the shorter leg and the hypontenuse is 5cm, then what are the lengths of the leg? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108396 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=108396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help<BR>\n" );
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document.write( "The longer leg of a right triangle is 1 cm. longer than the shorter leg and the hypontenuse is 5cm, then what are the lengths of the leg?<BR>\n" );
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document.write( "The shorter leg is represented by \"x\", the longer leg is (x+1)<BR>\n" );
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document.write( "We will use the Pythagorean theorem to solve for the two sides, the Pythagorean theorem equation is<BR>\n" );
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document.write( "<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" );
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document.write( "\"a\" and \"b\" are the sides, \"c\" is the hypontenuse. We will now replace \"a\", \"b\" , and \"c\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B1%29%5E2+%2B+x%5E2+=+5%5E2+ ALIGN=MIDDLE  ALT=\"+%28x%2B1%29%5E2+%2B+x%5E2+=+5%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B1%29%5E2+%2B+x%5E2+=+25+ ALIGN=MIDDLE  ALT=\"+%28x%2B1%29%5E2+%2B+x%5E2+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will solve it even more<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2+%2B+2x+%2B1%29+%2B+x%5E2+=+25+ ALIGN=MIDDLE  ALT=\"+%28x%5E2+%2B+2x+%2B1%29+%2B+x%5E2+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+2x+%2B1+%2B+x%5E2+=+25+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+2x+%2B1+%2B+x%5E2+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28x%29%5E2+%2B+2x+%2B1+=+25+ ALIGN=MIDDLE  ALT=\"+2%28x%29%5E2+%2B+2x+%2B1+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will move the \"25\" to the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28x%29%5E2+%2B+2x+%2B1+-25+=+25+-+25+ ALIGN=MIDDLE  ALT=\"+2%28x%29%5E2+%2B+2x+%2B1+-25+=+25+-+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28x%29%5E2+%2B+2x+-+24+=+0+ ALIGN=MIDDLE  ALT=\"+2%28x%29%5E2+%2B+2x+-+24+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can reduce the equation, we will divide everything by \"2\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%28x%29%5E2+%2B+2x+-+24%29%2F2+=+0%2F2+ ALIGN=MIDDLE  ALT=\"+%282%28x%29%5E2+%2B+2x+-+24%29%2F2+=+0%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+x+-+12+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+x+-+12+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can use the quadratic equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "This is the original equation using \"a\", \"b\", and \"c\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%28x%29%5E2+%2B+%28b%29x+%2B+c+=+0+ ALIGN=MIDDLE  ALT=\"+a%28x%29%5E2+%2B+%28b%29x+%2B+c+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+x+-+12+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+x+-+12+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "a = 1, b = 1, c = -12<BR>\n" );
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document.write( "Now we can replace them in the quadratic equation,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-12%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-12%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B-+sqrt%28+1-%28-48%29+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B-+sqrt%28+1-%28-48%29+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B-+sqrt%28+1+%2B+48%29%29%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B-+sqrt%28+1+%2B+48%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B-+sqrt+%2849%29+%29%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B-+sqrt+%2849%29+%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ". <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B-+7+%29%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B-+7+%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will use addition(if we used subtraction, the answer would be negative)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B+7+%29%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B+7+%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6%2F2+ ALIGN=MIDDLE  ALT=\"x+=+6%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3+ ALIGN=MIDDLE  ALT=\"x+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "x = 3 cm.( lengths or measurements can't be negative, the other answer would be (-4) )( you can check by replacing \"x\" in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B1%29%5E2+%2B+x%5E2+=+25+ ALIGN=MIDDLE  ALT=\"+%28x%2B1%29%5E2+%2B+x%5E2+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > with \"3\"<BR>\n" );
document.write( "or \"-4\"<BR>\n" );
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document.write( "The shorter side was x, or 3 cm., the longer side was (x+1), or 4 cm.<BR>\n" );
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document.write( "You can check by replacing \"a\" and \"b\" in the Pythagorean theorem equation<BR>\n" );
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document.write( "<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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%5E2+%2B+3%5E2+=+5%5E2+ ALIGN=MIDDLE  ALT=\"+4%5E2+%2B+3%5E2+=+5%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16+%2B+9+=+25+ ALIGN=MIDDLE  ALT=\"+16+%2B+9+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25+=+25+ ALIGN=MIDDLE  ALT=\"+25+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Shorter side = 3 cm.<BR>\n" );
document.write( "Longer side = 4 cm.<BR>\n" );
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document.write( "Hope I helped, Levi<BR>\n" );
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