document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011966>Question 1011966</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Have problems  with finding the  length and the ditance of a sqaure. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627796 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 14 an extension ;\r<BR>\n" );
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document.write( "ladder rests <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4m ALIGN=MIDDLE  ALT=\"4m\"   DISABLED_style= \"max-width:90%; height:auto;\" > up a wall<BR>\n" );
document.write( "If the ladder is extended a further <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.8 ALIGN=MIDDLE  ALT=\"0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > without moving the foot of the ladder, then it will now rest <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1m ALIGN=MIDDLE  ALT=\"1m\"   DISABLED_style= \"max-width:90%; height:auto;\" > further up the wall\r<BR>\n" );
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document.write( " How long is the extended ladder?\r<BR>\n" );
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document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > = original length of the ladder<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the distance of the foot of the ladder from the wall\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2+=+a%5E2+%2B+4%5E2 ALIGN=MIDDLE  ALT=\"L%5E2+=+a%5E2+%2B+4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2+=+a%5E2+%2B+16 ALIGN=MIDDLE  ALT=\"L%5E2+=+a%5E2+%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=a%5E2+=+L%5E2+-+16 ALIGN=MIDDLE  ALT=\"a%5E2+=+L%5E2+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- eq. 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L%2B0.8%29%5E2+=+a%5E2+%2B+%284%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"%28L%2B0.8%29%5E2+=+a%5E2+%2B+%284%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "subs <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from eq. 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L%2B0.8%29%5E2+=+L%5E2+-+16+%2B+5%5E2 ALIGN=MIDDLE  ALT=\"%28L%2B0.8%29%5E2+=+L%5E2+-+16+%2B+5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28L%5E2%29+%2B+1.6L+%2B+0.64+=+cross%28L%5E2%29+-+16+%2B+25 ALIGN=MIDDLE  ALT=\"cross%28L%5E2%29+%2B+1.6L+%2B+0.64+=+cross%28L%5E2%29+-+16+%2B+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6L+%2B+0.64+=+9 ALIGN=MIDDLE  ALT=\"1.6L+%2B+0.64+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6L+=+8.36 ALIGN=MIDDLE  ALT=\"1.6L+=+8.36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28L+=+5.23m%29 ALIGN=MIDDLE  ALT=\"highlight%28L+=+5.23m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2B0.8+=5.23m%2B0.8m+=6.03m ALIGN=MIDDLE  ALT=\"L%2B0.8+=5.23m%2B0.8m+=6.03m\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- length of extended ladder\r<BR>\n" );
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document.write( "15) \r<BR>\n" );
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document.write( "an equilateral triangle has area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=16sqrt%283%29cm%5E2 ALIGN=MIDDLE  ALT=\"A=16sqrt%283%29cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "Find the length of its sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%281%2F2%29bh ALIGN=MIDDLE  ALT=\"A+=+%281%2F2%29bh\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Asqrt%283%29+=+%281%2F2%29bh ALIGN=MIDDLE  ALT=\"16%2Asqrt%283%29+=+%281%2F2%29bh\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=bh+=+32sqrt%283%29 ALIGN=MIDDLE  ALT=\"bh+=+32sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........eq.1\r<BR>\n" );
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document.write( "-----------<BR>\n" );
document.write( "Find altitude  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > in terms of side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "Since the triangle is equilateral, all sides are \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\":<BR>\n" );
document.write( "Draw an altitude from the vertex to the base.<BR>\n" );
document.write( "You have a right triangle with base = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F2 ALIGN=MIDDLE  ALT=\"b%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and hypotenuse = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The altitude is the 3rd side:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+%28b%2F2%29%5E2+%2B+h%5E2 ALIGN=MIDDLE  ALT=\"b%5E2+=+%28b%2F2%29%5E2+%2B+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-%28b%2F2%29%5E2+=+h%5E2 ALIGN=MIDDLE  ALT=\"b%5E2-%28b%2F2%29%5E2+=+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-b%5E2%2F4+=+h%5E2 ALIGN=MIDDLE  ALT=\"b%5E2-b%5E2%2F4+=+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29b%5E2+=+h%5E2 ALIGN=MIDDLE  ALT=\"%283%2F4%29b%5E2+=+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%283%2F4%29b%5E2%29+=+h ALIGN=MIDDLE  ALT=\"sqrt%28%283%2F4%29b%5E2%29+=+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2F2%29b+=+h ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2F2%29b+=+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute in eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=bh+=+32sqrt%283%29 ALIGN=MIDDLE  ALT=\"bh+=+32sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2A%28sqrt%283%29%2F2%29b+=+32sqrt%283%29 ALIGN=MIDDLE  ALT=\"b%2A%28sqrt%283%29%2F2%29b+=+32sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=+32sqrt%283%29%2F%28sqrt%283%29%2F2%29+ ALIGN=MIDDLE  ALT=\"b%5E2=+32sqrt%283%29%2F%28sqrt%283%29%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=+%282%2A32cross%28sqrt%283%29%29%29%2Fcross%28sqrt%283%29%29+ ALIGN=MIDDLE  ALT=\"b%5E2=+%282%2A32cross%28sqrt%283%29%29%29%2Fcross%28sqrt%283%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=+64+ ALIGN=MIDDLE  ALT=\"b%5E2=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%2864%29 ALIGN=MIDDLE  ALT=\"b=sqrt%2864%29\"   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=highlight%28b=8%29 ALIGN=MIDDLE  ALT=\"highlight%28b=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >->the length of each side\r<BR>\n" );
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document.write( "and now we can find the length of altitude too:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2F2%298+=+h ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2F2%298+=+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%283%29=+h ALIGN=MIDDLE  ALT=\"4%2Asqrt%283%29=+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check the area:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%281%2F2%29bh ALIGN=MIDDLE  ALT=\"A+=+%281%2F2%29bh\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%281%2F2%298%2A4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"A+=+%281%2F2%298%2A4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%281%2Fcross%282%291%29cross%288%294%2A4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"A+=+%281%2Fcross%282%291%29cross%288%294%2A4%2Asqrt%283%29\"   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=A+=+16sqrt%283%29 ALIGN=MIDDLE  ALT=\"A+=+16sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which confirms our solution\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );