document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205403>Question 1205403</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A town map shows the location of its school (S), municipal hall (H), church (C), and market (M). When these places are combined they form the shape of an isosceles trapezoid with an area of 475 sq. meters. The school (S) is adjacent to the municipal hall (H) and diagonally across to the church (C) (Note: SH is one of the non-parallel sides). The school (S) is 16 meters away from the market (M) and the municipal hall (H) is 22 meters away from the church (C). Suppose your house (E) is opposite the school and located in between the municipal hall and church, then how far is it from the school? Provide Illustration, Working Equation, Solution, and Answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842179 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=842179\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I interpret the phrasing \"<font color=blue>Suppose your house (E) is opposite the school</font>\" to mean \"points E and S are on the same vertical line\".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-2%2C8%2C-3%2C7%2C%0D%0Acircle%285%2C1%2C0.05%29%2Ccircle%285%2C1%2C0.07%29%2Ccircle%285%2C1%2C0.09%29%2Ccircle%285%2C1%2C0.11%29%2Ccircle%285%2C1%2C0.13%29%2Ccircle%285%2C1%2C0.15%29%2Ccircle%282%2C1%2C0.05%29%2Ccircle%282%2C1%2C0.07%29%2Ccircle%282%2C1%2C0.09%29%2Ccircle%282%2C1%2C0.11%29%2Ccircle%282%2C1%2C0.13%29%2Ccircle%282%2C1%2C0.15%29%2Ccircle%281%2C1%2C0.05%29%2Ccircle%281%2C1%2C0.07%29%2Ccircle%281%2C1%2C0.09%29%2Ccircle%281%2C1%2C0.11%29%2Ccircle%281%2C1%2C0.13%29%2Ccircle%281%2C1%2C0.15%29%2Ccircle%284%2C3%2C0.05%29%2Ccircle%284%2C3%2C0.07%29%2Ccircle%284%2C3%2C0.09%29%2Ccircle%284%2C3%2C0.11%29%2Ccircle%284%2C3%2C0.13%29%2Ccircle%284%2C3%2C0.15%29%2Ccircle%282%2C3%2C0.05%29%2Ccircle%282%2C3%2C0.07%29%2Ccircle%282%2C3%2C0.09%29%2Ccircle%282%2C3%2C0.11%29%2Ccircle%282%2C3%2C0.13%29%2Ccircle%282%2C3%2C0.15%29%2C%0D%0A%0D%0Aline%281%2C1%2C2%2C3%29%2Cline%282%2C3%2C4%2C3%29%2Cline%284%2C3%2C5%2C1%29%2Cline%285%2C1%2C1%2C1%29%2Cline%282%2C1%2C2%2C3%29%2C%0D%0A%0D%0A%0D%0Alocate%280.56%2C0.84%2C%22H%22%29%2Clocate%281.7%2C3.22%2B0.2%2C%22S%22%29%2Clocate%284.28%2C3.22%2C%22M%22%29%2Clocate%285.24%2C0.82%2C%22C%22%29%2Clocate%282.06%2C0.82%2C%22E%22%29%2C%0D%0A%0D%0Alocate%28-2%2C-2%2Cmatrix%281%2C4%2C%22Diagram%22%2C%22not%22%2C%22to%22%2C%22scale%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "S = school<BR>\n" );
document.write( "H = municipal hall<BR>\n" );
document.write( "C = church<BR>\n" );
document.write( "M = market<BR>\n" );
document.write( "E = your house\r<BR>\n" );
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document.write( "My drawing is almost the same as tutor Theo's drawing, except point E has been moved to the left to be directly under point S. Also, point D is not needed. \r<BR>\n" );
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document.write( "Recall the area of a trapezoid is:<BR>\n" );
document.write( "area = 0.5*height*(base1+base2)<BR>\n" );
document.write( "where base1 and base2 are the parallel sides.\r<BR>\n" );
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document.write( "In this case, SM = 16 and HC = 22 are the parallel sides.<BR>\n" );
document.write( "The goal is to find the distance from your house (E) to your school (S). <BR>\n" );
document.write( "In other words, we want to find the length of segment ES.<BR>\n" );
document.write( "But notice that segment ES is the height of the trapezoid.<BR>\n" );
document.write( "x = height = length of ES\r<BR>\n" );
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document.write( "area = 0.5*height*(base1+base2)<BR>\n" );
document.write( "area = 0.5*ES*(SM+HC)<BR>\n" );
document.write( "475 = 0.5*x*(16+22)<BR>\n" );
document.write( "I'll let the student take over from here.<BR>\n" );
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