document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41947>Question 41947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the following ewuation and compute the area it encloses:<BR>\n" );
document.write( "abs(2x -10) + abs (5y - 10) = 20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27113 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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/cgi-bin/show-face.mpl?user=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graph the following ewuation and compute the area it encloses:<BR>\n" );
document.write( "abs(2x -10) + abs (5y - 10) = 20\r<BR>\n" );
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document.write( "When x < 5, 2x < 10 or |2x - 10| = 10 - 2x<BR>\n" );
document.write( "i) When y < 2, 5y < 10 or |5y - 10| = 10 - 5y. So the given equation becomes 2x + 5y = 0 (brown).<BR>\n" );
document.write( "ii) When y > 2, 5y > 10 or |5y - 10| = 5y - 10. So the given equation becomes 2x - 5y + 20 = 0 (green).\r<BR>\n" );
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document.write( "When x > 5, 2x > 10 or |2x - 10| = 2x - 10<BR>\n" );
document.write( "i) When y < 2, 5y < 10 or |5y - 10| = 10 - 5y. So the given equation becomes 2x - 5y = 20 (blue).<BR>\n" );
document.write( "ii) When y > 2, 5y > 10 or |5y - 10| = 5y - 10. So the given equation becomes 2x + 5y  = 40 (violet).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-25%2C25%2C-25%2C25%2C+-0.4%2Ax%2C0.4%2Ax%2B4%2C0.4%2Ax-4%2C8-0.4%2Ax%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-25%2C25%2C-25%2C25%2C+-0.4%2Ax%2C0.4%2Ax%2B4%2C0.4%2Ax-4%2C8-0.4%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From the graph find the coordinates of the points of intersection of the straight lines.<BR>\n" );
document.write( "The coordinates of the points of intersection of the brown and green lines are (-5,2).<BR>\n" );
document.write( "The coordinates of the points of intersection of the brown and blue lines are (5,-2).<BR>\n" );
document.write( "The coordinates of the points of intersection of the blue and violet lines are (15,2).<BR>\n" );
document.write( "The coordinates of the points of intersection of the violet and green lines are (5,6).<BR>\n" );
document.write( "So, clearly, the quadrilateral formed by the intersection of the straight lines is a rhombus.<BR>\n" );
document.write( "The diagonals of this rhombus are 8 and 20 units respectively.<BR>\n" );
document.write( "Hence the reqd. area = area of the rhombus = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > x 8 x 20 = 80 sq units. </SPAN>\n" );
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