document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79830>Question 79830</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not sure what category this problem should be under, please help!\r<BR>\n" );
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document.write( "Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilize the door by attaching a steel cable diagonally. If the cable measures  &#8730;194/2 ft, what are the dimensions of the door? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57283 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=57283\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your problem tells you that the height (H) of rectangular screen door is 4 feet more than<BR>\n" );
document.write( "its width (W).  In equation form this becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+W+%2B+4 ALIGN=MIDDLE  ALT=\"H+=+W+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The problem also tells you that the diagonal (D) of this rectangular door is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%28194%29%2F2 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28194%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and (calculator time) the square root of 194 is 13.92838828.  Divide this by 2 and you<BR>\n" );
document.write( "find that the diagonal of the door (in feet) is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+6.964194139 ALIGN=MIDDLE  ALT=\"D+=+6.964194139\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can apply the Pythagorean theorem which says that for a right triangle (formed<BR>\n" );
document.write( "by the height, the width, and the diagonal of the door), the sum of the squares of each<BR>\n" );
document.write( "of the legs of the triangle equals the square of the diagonal.  For this problem you can<BR>\n" );
document.write( "write the equation that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2+%2B+W%5E2+=+D%5E2 ALIGN=MIDDLE  ALT=\"H%5E2+%2B+W%5E2+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But from your first steps on this problem you know that H = W + 4, so you can substitute<BR>\n" );
document.write( "W + 4 for H and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28W%2B4%29%5E2+%2B+W%5E2+=+D%5E2 ALIGN=MIDDLE  ALT=\"%28W%2B4%29%5E2+%2B+W%5E2+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Square the (W + 4) term on the left and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28W%5E2+%2B+8W+%2B+16%29+%2B+W%5E2+=+D%5E2 ALIGN=MIDDLE  ALT=\"%28W%5E2+%2B+8W+%2B+16%29+%2B+W%5E2+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5E2 ALIGN=MIDDLE  ALT=\"W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms on the left side and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%5E2+%2B+8W+%2B+16+=+D%5E2 ALIGN=MIDDLE  ALT=\"2W%5E2+%2B+8W+%2B+16+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next recall that earlier you found that the diagonal D was 6.964194139 feet.  Square this <BR>\n" );
document.write( "and you get that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2+=+%286.964194139%29%5E2+=+48.5 ALIGN=MIDDLE  ALT=\"D%5E2+=+%286.964194139%29%5E2+=+48.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In the quadratic equation substitute 48.5 for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2 ALIGN=MIDDLE  ALT=\"D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%5E2+%2B+8W+%2B+16+=+48.5 ALIGN=MIDDLE  ALT=\"2W%5E2+%2B+8W+%2B+16+=+48.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get this into standard quadratic form by subtracting 48.5 from both sides.  The result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%5E2+%2B+8W+-+32.5+=+0 ALIGN=MIDDLE  ALT=\"2W%5E2+%2B+8W+-+32.5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Although you do not need to do this next step, you can make the problem a little easier<BR>\n" );
document.write( "by dividing both sides by 2 just to eliminate the 2 that multiplies the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5E2 ALIGN=MIDDLE  ALT=\"W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term.<BR>\n" );
document.write( "When you do that division the quadratic equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5E2+%2B+4W+-+16.25+=+0 ALIGN=MIDDLE  ALT=\"W%5E2+%2B+4W+-+16.25+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can apply the quadratic formula to solve this equation.  The quadratic formula<BR>\n" );
document.write( "says that for a quadratic equation of the form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the two solutions will be:<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( "By comparing your equation with the standard form you see that the corresponding factors<BR>\n" );
document.write( "are: x = W, a = +1, b = +4, and c = -16.25<BR>\n" );
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document.write( "Substitute these values into the solution equation and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-%28%2B4%29+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-16.25%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"W+=+%28-%28%2B4%29+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-16.25%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-4+%2B-+sqrt%2816+%2B+65%29%29%2F2 ALIGN=MIDDLE  ALT=\"W+=+%28-4+%2B-+sqrt%2816+%2B+65%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The term in the radical is 81 and its square root is 9.  This simplifies your equation<BR>\n" );
document.write( "to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-4+%2B-+9%29%2F2+ ALIGN=MIDDLE  ALT=\"W+=+%28-4+%2B-+9%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This means your possible solutions are:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-4-9%29%2F2+=+-13%2F2+=+-6.5 ALIGN=MIDDLE  ALT=\"W+=+%28-4-9%29%2F2+=+-13%2F2+=+-6.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-4%2B9%29%2F2=+5%2F2+=+2.5 ALIGN=MIDDLE  ALT=\"W+=+%28-4%2B9%29%2F2=+5%2F2+=+2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can ignore the first solution because it is negative and having a negative width<BR>\n" );
document.write( "for a screen door doesn't make sense.  The second solution means that the width of the<BR>\n" );
document.write( "door is 2.5 feet (or 30 inches).  A little narrow by today's standard construction<BR>\n" );
document.write( "but a reasonable answer.  The height is 4 feet more than that (from your work at the<BR>\n" );
document.write( "start of the problem) and that means the door is 2.5 + 4 = 6.5 feet (78 inches) tall.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
document.write( ". </SPAN>\n" );
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