document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=863534>Question 863534</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area of an isoceles trapeziod that has a perimeter of 90 meters. The longer base is 5 meters less than twice the length of the shorter base. The length of each leg is 3 meters less than the length of the shorter base.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #520475 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=520475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b, bottom base, the longer base<BR>\n" );
document.write( "t, top base<BR>\n" );
document.write( "y, each side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-5%2B2t ALIGN=MIDDLE  ALT=\"b=-5%2B2t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2Bt ALIGN=MIDDLE  ALT=\"y=-3%2Bt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "SUM of the lengths of the sides is 90 meters, according to \"perimeter of 90 meters\".  Notice how b and y are described in terms of t.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90=%28-5%2B2t%29%2Bt%2B2%28-3%2Bt%29 ALIGN=MIDDLE  ALT=\"90=%28-5%2B2t%29%2Bt%2B2%28-3%2Bt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2B2t%2Bt%2B2t-5=90 ALIGN=MIDDLE  ALT=\"-6%2B2t%2Bt%2B2t-5=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5t-11=90 ALIGN=MIDDLE  ALT=\"5t-11=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5t=101 ALIGN=MIDDLE  ALT=\"5t=101\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=101%2F5%29 ALIGN=MIDDLE  ALT=\"highlight%28t=101%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The base angle at bottom is needed, so that the height can be found.  This isosceles trapezoid is composed of two right triangles, one on each side, and a rectangle in the middle.  You can draw this figure.\r<BR>\n" );
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document.write( "Call the base angle, measure a.<BR>\n" );
document.write( "Let h = height of the triangle and also of the trapezoid.<BR>\n" );
document.write( "The bottom leg OF EACH RIGHT TRIANGLE is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-t%29%2F2 ALIGN=MIDDLE  ALT=\"%28b-t%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; and since you have a formula for b and have now found t, each bottom leg of the right triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282t-5%29-t%29%2F2 ALIGN=MIDDLE  ALT=\"%28%282t-5%29-t%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t-5%29%2F2 ALIGN=MIDDLE  ALT=\"%28t-5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28101%2F5-5%29%2F2 ALIGN=MIDDLE  ALT=\"%28101%2F5-5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28101-25%29%2F%285%2A2%29 ALIGN=MIDDLE  ALT=\"%28101-25%29%2F%285%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76%2F10 ALIGN=MIDDLE  ALT=\"76%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2838%2F5%29 ALIGN=MIDDLE  ALT=\"highlight_green%2838%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, leg length of a right triangle.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "The hypotenuse of each right triangle is y.  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%29=%2838%2F5%29%2Fy ALIGN=MIDDLE  ALT=\"cos%28a%29=%2838%2F5%29%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and a formula for y is already described in terms of t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2838%2F5%29%2F%28t-3%29=cos%28a%29 ALIGN=MIDDLE  ALT=\"%2838%2F5%29%2F%28t-3%29=cos%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2838%2F5%29%2F%28101%2F5-3%29=cos%28a%29 ALIGN=MIDDLE  ALT=\"%2838%2F5%29%2F%28101%2F5-3%29=cos%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2838%2F5%29%2F%28101%2F5-15%2F5%29=cos%28a%29 ALIGN=MIDDLE  ALT=\"%2838%2F5%29%2F%28101%2F5-15%2F5%29=cos%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2838%2F5%29%2F%2886%2F5%29=cos%28a%29 ALIGN=MIDDLE  ALT=\"%2838%2F5%29%2F%2886%2F5%29=cos%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%29=38%2F86 ALIGN=MIDDLE  ALT=\"cos%28a%29=38%2F86\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=63.8%29 ALIGN=MIDDLE  ALT=\"highlight%28a=63.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h=y%2Asin%2863.8%29%29 ALIGN=MIDDLE  ALT=\"highlight%28h=y%2Asin%2863.8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=%28t-3%29sin%2863.8%29 ALIGN=MIDDLE  ALT=\"h=%28t-3%29sin%2863.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=%28101%2F5-3%29sin%2863.8%29 ALIGN=MIDDLE  ALT=\"h=%28101%2F5-3%29sin%2863.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h=%2886%2F5%29sin%2863.8%29%29 ALIGN=MIDDLE  ALT=\"highlight%28h=%2886%2F5%29sin%2863.8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----The HEIGHT of the trapezoid.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "AREA:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28b%2Bt%29%2F2%29h ALIGN=MIDDLE  ALT=\"%28%28b%2Bt%29%2F2%29h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282t-5%2Bt%29%2F2%29%2886%2F5%29sin%2863.8%29 ALIGN=MIDDLE  ALT=\"%28%282t-5%2Bt%29%2F2%29%2886%2F5%29sin%2863.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283t-5%29%2F2%29%2886%2F5%29sin%2863.8%29 ALIGN=MIDDLE  ALT=\"%28%283t-5%29%2F2%29%2886%2F5%29sin%2863.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%28101%2F5%29-5%29%2F2%29%2886%2F5%29sin%2863.8%29 ALIGN=MIDDLE  ALT=\"%28%283%28101%2F5%29-5%29%2F2%29%2886%2F5%29sin%2863.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".... you can finish this computation. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );