document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165102>Question 1165102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An isosceles trapezium ABCD has perpendicular diagonals and side lengths<BR>\n" );
document.write( "AB = 1 and CD = 7.<BR>\n" );
document.write( "(a) Find the length of the two equal sides.<BR>\n" );
document.write( "(b) Find the product of the lengths of the diagonals. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789573 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solver91311&illustration_name=Trapezium.jpg\">.\r<BR>\n" );
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document.write( "In order for the trapezium to be isosceles, the segment AB must be centered over segment CD. So placing the figure on a coordinate axis with D at the origin and C at (7,0), means that the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinates of A and B must be 3 and 4 respectively.  Now we need to determine the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-coordinate of A and B.\r<BR>\n" );
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document.write( "Since the diagonals are perpendicular, the slopes of the lines containing segments AC and DB must be negative reciprocal.  Use the slope formula to get expressions for these two slopes in terms of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\">, then set the negative reciprocal of one equal to the other one and solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\">.\r<BR>\n" );
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document.write( "Using the coordinates of A and D gives you the measure of the sides of a right triangle with AD as the hypotenuse.  Use Pythagoras to calculate the measure of AD.  Check your work by doing the same calculation for the other side.\r<BR>\n" );
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document.write( "Part b is calculated similarly.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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