document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1064331>Question 1064331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A landscape architect is making a path between two trees, A and B, that are 60 feet apart. He wants the path to be 70 feet long and to contain one right angle, as shown. Write an equation to determine how long the legs of the path should be. Find the lengths to the nearest tenth of a foot. (Note: will need to solve using the quadratic formula) \r<BR>\n" );
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document.write( "I tried to solve using x^2 +(70-x)^2 = 60^2 and ended up with one side as 9.3 and the other as 60.7 but I am confused because I did not have to use the quadratic formula. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #679377 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=679377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Just one right angle opposite of the 60 foot distance between the two trees;  being hypotenuse of a right triangle, same as half of a rectangle.  Path length wanted, 70 feet.\r<BR>\n" );
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document.write( "Let x be one of the leg lengths.  The other leg length is 70-x.\r<BR>\n" );
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document.write( "Your equation is correct.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%2870-x%29%5E2=60%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%2870-x%29%5E2=60%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify and solve.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B70%5E2-140x%2Bx%5E2=3600 ALIGN=MIDDLE  ALT=\"x%5E2%2B70%5E2-140x%2Bx%5E2=3600\"   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=2x%5E2-140x%2B70%5E2-3600=0 ALIGN=MIDDLE  ALT=\"2x%5E2-140x%2B70%5E2-3600=0\"   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=2x%5E2-140x%2B4900-3600=0 ALIGN=MIDDLE  ALT=\"2x%5E2-140x%2B4900-3600=0\"   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=x%5E2-70x%2B650=0 ALIGN=MIDDLE  ALT=\"x%5E2-70x%2B650=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Can the quadratic be factored?\r<BR>\n" );
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document.write( "No.<BR>\n" );
document.write( "Discriminant  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4900-4%2A650=2300=10%5E2%2A23 ALIGN=MIDDLE  ALT=\"4900-4%2A650=2300=10%5E2%2A23\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "General Solution Formula for a Quadratic Equation.....<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2870%2B-+10%2Asqrt%2823%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x=%2870%2B-+10%2Asqrt%2823%29%29%2F%282%2A2%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=x=%2835%2B-+5%2Asqrt%2823%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2835%2B-+5%2Asqrt%2823%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x=5.510  or  x=29.490<BR>\n" );
document.write( "You can check if these work in the original <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%2870-x%29%5E2=60%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%2870-x%29%5E2=60%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > equation or not. </SPAN>\n" );
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