document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105914>Question 1105914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the lengths of the bases of an isosceles trapezoid is a circle are 10 cm and 22 cm, and if one of the legs is 10 cm, then what is the length of the diagonal in cm? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720813 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=720813\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the lengths of the bases of an isosceles trapezoid are 10 cm and 22 cm,<BR>\n" );
document.write( "and if one of the legs' length is 10 cm,<BR>\n" );
document.write( "then the other leg's length is also 10 cm,<BR>\n" );
document.write( "or else it is not really isosceles.<BR>\n" );
document.write( "The trapezoid is sketched below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C300%2C-12%2C12%2C-2%2C10%2C%0D%0Agreen%28rectangle%28-5%2C0%2C5%2C8%29%29%2C%0D%0Agreen%28rectangle%28-5%2C0%2C-5.4%2C0.4%29%29%2Cgreen%28rectangle%285%2C0%2C5.4%2C0.4%29%29%2C%0D%0Aline%28-11%2C0%2C11%2C0%29%2Cline%28-5%2C8%2C5%2C8%29%2C%0D%0Aline%28-11%2C0%2C-5%2C8%29%2Cline%2811%2C0%2C5%2C8%29%2C%0D%0Alocate%28-11.5%2C0%2CA%29%2Clocate%2811.2%2C0%2CD%29%2C%0D%0Alocate%28-5.5%2C8.5%2CB%29%2Clocate%285.2%2C8.5%2CC%29%2C%0D%0Alocate%28-5.1%2C0%2CF%29%2Clocate%284.9%2C0%2CE%29%2C%0D%0Alocate%28-8%2C4%2C10cm%29%2Clocate%286.8%2C4%2C10cm%29%2C%0D%0Alocate%28-0.5%2C8%2C10cm%29%2Clocate%28-0.5%2C0.6%2C10cm%29%2C%0D%0Alocate%28-8.5%2C0.6%2C6cm%29locate%287.5%2C0.6%2C6cm%29%2C%0D%0Alocate%28-4.9%2C4.4%2Cgreen%28h%29%29%2Clocate%285.1%2C4.4%2Cgreen%28h%29%29%2C%0D%0Alocate%28-0.5%2C-0.7%2C22cm%29%2Carrow%28-1%2C-1%2C-11%2C-1%29%2Carrow%281%2C-1%2C11%2C-1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The green lines, perpendicular to the bases,<BR>\n" );
document.write( "split the isosceles trapezoid into rectangle BCEF,<BR>\n" );
document.write( "and right triangles ABF and CDE.<BR>\n" );
document.write( "We know the length of all the segments in the sketch, except for the green ones.<BR>\n" );
document.write( "Their length, according to the Pythagorean theorem, is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28h%29=sqrt%28%2810cm%29%5E2-%286cm%29%5E2%29=8cm ALIGN=MIDDLE  ALT=\"green%28h%29=sqrt%28%2810cm%29%5E2-%286cm%29%5E2%29=8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That allows us to calculate the length of diagonal AC<BR>\n" );
document.write( "which is the hypotenuse of right triangle ACE.<BR>\n" );
document.write( "We use the Pythagorean theorem again, to calculate that length as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28AE%29%5E2%2B%28CE%29%5E2%29=sqrt%28%2816cm%29%5E2%2B%2810cm%29%5E2%29=sqrt%28356%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm=4sqrt%2889%29 ALIGN=MIDDLE  ALT=\"cm=4sqrt%2889%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > or approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2818.9cm%29 ALIGN=MIDDLE  ALT=\"highlight%2818.9cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );