document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697554>Question 697554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the length of one leg of a right triangle is 17cm more than that of the other leg. The length of the hypotenue is 4 vm more than triple that of the shorter leg. Find the lenghts of each of the three sides </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430125 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=430125\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the shorter leg. Then the longer leg would be (x + 17) and the hypotenuse would be (3x + 4). In order for this to be a right triangle these sides must fit the Pythagorean equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%5E2+%2B+%28x%2B17%29%5E2+=+%283x%2B4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%29%5E2+%2B+%28x%2B17%29%5E2+=+%283x%2B4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we solve for x. First we simplify. (Be sure to use FOIL or the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern to square the x+17 and the 3x+4.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x%5E2%2B2%2Ax%2A17%2B17%5E2+=+%283x%29%5E2+%2B+2%283x%29%284%29+%2B4%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x%5E2%2B2%2Ax%2A17%2B17%5E2+=+%283x%29%5E2+%2B+2%283x%29%284%29+%2B4%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%2B34x%2B289+=+9x%5E2+%2B+24x+%2B+16 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x%5E2%2B34x%2B289+=+9x%5E2+%2B+24x+%2B+16\"   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%2B34x%2B289+=+9x%5E2+%2B+24x+%2B+16 ALIGN=MIDDLE  ALT=\"2x%5E2%2B34x%2B289+=+9x%5E2+%2B+24x+%2B+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since this is a quadratic equation we want one side to be zero. Subtracting the entire left side from each side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+7x%5E2-10x-273 ALIGN=MIDDLE  ALT=\"0+=+7x%5E2-10x-273\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This will factor, but not easily. So you may prefer to use the Quadratic Formula instead.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%287x%2B39%29%28x-7%29 ALIGN=MIDDLE  ALT=\"0+=+%287x%2B39%29%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the Zero Product Property:<BR>\n" );
document.write( "7x + 39 = 0 or x - 7 = 0<BR>\n" );
document.write( "Solving these we get:<BR>\n" );
document.write( "x = -39/7 or x = 7<BR>\n" );
document.write( "We will reject the first solution not because it is a fraction but because it is negative. x is the length of the shorter leg and we cannot have negative lengths.<br><BR>\n" );
document.write( "So the shorter leg is 7 cm.<BR>\n" );
document.write( "The longer leg would be x + 17 = 7 + 17 = 24 cm<BR>\n" );
document.write( "And the hypotenuse would be 3x + 4 = 3(7) + 4 = 21 + 4 = 25 cm </SPAN>\n" );
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