document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149701>Question 149701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The dimensions of rectangle ABCD are AB=12 and BC=16.  Point P is marked on side BC so that BP=5, and the intersection of AP and BD is called T.  Find the lengths of the four segments TA, TP, TB, and TD.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109812 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=109812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First draw the rectangle with the point P\r<BR>\n" );
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document.write( "Now draw in the segments AP, BD, and PD. Take note of the unknown variables I'm assigning. If you look closely, you'll notice that a trapezoid forms due to these extra lines segments. Through the use of pythagoreans theorem, we get the length of AP of 13 and BD of 20\r<BR>\n" );
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document.write( "Now, it turns out that the ratio of the parallel sides 5 and 16 are the same as the ratio of the lengths of the cut diagonals. So the following ratios are true:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F16=x%2F%2813-x%29 ALIGN=MIDDLE  ALT=\"5%2F16=x%2F%2813-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F16=y%2F%2820-y%29 ALIGN=MIDDLE  ALT=\"5%2F16=y%2F%2820-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So let's solve for x:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%2F%2816%29=%28x%29%2F%2813-x%29 ALIGN=MIDDLE  ALT=\"%285%29%2F%2816%29=%28x%29%2F%2813-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first ratio\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%2813-x%29=%28x%29%2816%29 ALIGN=MIDDLE  ALT=\"%285%29%2813-x%29=%28x%29%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65-5x=16x ALIGN=MIDDLE  ALT=\"65-5x=16x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x=16x-65 ALIGN=MIDDLE  ALT=\"-5x=16x-65\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65 ALIGN=MIDDLE  ALT=\"65\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x-16x=-65 ALIGN=MIDDLE  ALT=\"-5x-16x=-65\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x ALIGN=MIDDLE  ALT=\"16x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-21x=-65 ALIGN=MIDDLE  ALT=\"-21x=-65\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-65%29%2F%28-21%29 ALIGN=MIDDLE  ALT=\"x=%28-65%29%2F%28-21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-21 ALIGN=MIDDLE  ALT=\"-21\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=65%2F21 ALIGN=MIDDLE  ALT=\"x=65%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So the approximate length of x is 3.095 units. This means that TP is 3.095 units. This means that the other length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13-3.095=9.905 ALIGN=MIDDLE  ALT=\"13-3.095=9.905\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So TA is 9.905 units.\r<BR>\n" );
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document.write( "Now let's solve for y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%2F%2816%29=%28y%29%2F%2820-y%29 ALIGN=MIDDLE  ALT=\"%285%29%2F%2816%29=%28y%29%2F%2820-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second ratio\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%2820-y%29=%28y%29%2816%29 ALIGN=MIDDLE  ALT=\"%285%29%2820-y%29=%28y%29%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100-5y=16y ALIGN=MIDDLE  ALT=\"100-5y=16y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5y=16y-100 ALIGN=MIDDLE  ALT=\"-5y=16y-100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5y-16y=-100 ALIGN=MIDDLE  ALT=\"-5y-16y=-100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16y ALIGN=MIDDLE  ALT=\"16y\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-21y=-100 ALIGN=MIDDLE  ALT=\"-21y=-100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-100%29%2F%28-21%29 ALIGN=MIDDLE  ALT=\"y=%28-100%29%2F%28-21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-21 ALIGN=MIDDLE  ALT=\"-21\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=y=100%2F21 ALIGN=MIDDLE  ALT=\"y=100%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So the approximate length of y is 4.762 which means that the other length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20-4.762=15.238 ALIGN=MIDDLE  ALT=\"20-4.762=15.238\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So TB is 4.762 units and TD is 15.238 units.\r<BR>\n" );
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