document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=566135>Question 566135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a word problem on a sheet that I don't really understand. I would really love to know the steps to solving it since there are more of them. I've tried the pythagorean theorem, but I don't think I'm doing it right. I would greatly appreciate any help I receive.\r<BR>\n" );
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document.write( "In a square, the length of a side is 6 cm less than a diagonal. How long is each diagonal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #366134 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=366134\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a square, the length of a side is 6 cm less than a diagonal.<BR>\n" );
document.write( " How long is each diagonal?<BR>\n" );
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document.write( "Let c = the diagonal<BR>\n" );
document.write( "then<BR>\n" );
document.write( "a = the side of the square<BR>\n" );
document.write( "then<BR>\n" );
document.write( "c = (a+6)<BR>\n" );
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document.write( "Using pythag: a^2 + b^2 = c^2, (you're right about that!)<BR>\n" );
document.write( "It's a square so a = b, so we can write it <BR>\n" );
document.write( "2a^2 = (a+6)^2<BR>\n" );
document.write( "FOIL (a+6)(a+6)<BR>\n" );
document.write( "2a^2 = a^2 + 6a + 6a + 36<BR>\n" );
document.write( "2a^2 = a^2 + 12a + 36<BR>\n" );
document.write( "Combine like terms on the left<BR>\n" );
document.write( "2a^2 - a^2 - 12a - 36 = 0<BR>\n" );
document.write( "a^2 - 12a - 36 = 0<BR>\n" );
document.write( "Use the quadratic formula<BR>\n" );
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" );
document.write( "in this equation, x=a; a=1, b=-12, c=-36<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-%28-12%29+%2B-+sqrt%28-12%5E2-4%2A1%2A-36+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"a+=+%28-%28-12%29+%2B-+sqrt%28-12%5E2-4%2A1%2A-36+%29%29%2F%282%2A1%29+\"   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=a+=+%2812+%2B-+sqrt%28144-%28-144%29+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"a+=+%2812+%2B-+sqrt%28144-%28-144%29+%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=a+=+%2812+%2B-+sqrt%28288+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"a+=+%2812+%2B-+sqrt%28288+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "we only want the positive solution here<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%2812+%2B+16.97%29%2F2+ ALIGN=MIDDLE  ALT=\"a+=+%2812+%2B+16.97%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28.97%2F2 ALIGN=MIDDLE  ALT=\"28.97%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 14.5 cm is the length of the side<BR>\n" );
document.write( "but they want the diagonal<BR>\n" );
document.write( "14.5 + 6 = 20.5 cm is the length of the diagonal<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this on your calc: enter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2814.5%5E2+%2B+14.5%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2814.5%5E2+%2B+14.5%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > results: 20.5   <BR>\n" );
document.write( " </SPAN>\n" );
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