document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=777654>Question 777654</A>: <I><SPAN STYLE=\"word-break: break-all;\"> EAch of the two congruent sides of an isosceles triangle is 7 cm longer than half the base.  Find the length of each side of the triangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #474236 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=474236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are two many triangles, with different measurements that comply with that.<BR>\n" );
document.write( "Here are 3 examples:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-11%2C14%2C-1%2C24%2C%0D%0Agreen%28line%28-5%2C19%2C3.8%2C19%29%29%2Cgreen%28rectangle%28-5%2C19%2C-4.5%2C19.5%29%29%2C%0D%0Agreen%28line%2813%2C14%2C2.1%2C14%29%29%2Cgreen%28rectangle%2813%2C14%2C12.3%2C14.7%29%29%2C%0D%0Agreen%28line%280%2C0%2C0%2C13.7%29%29%2Cgreen%28rectangle%280%2C0%2C0.7%2C0.7%29%29%2C%0D%0Atriangle%28-10%2C0%2C10%2C0%2C0%2C13.7%29%2C%0D%0Atriangle%282.1%2C14%2C13%2C9%2C13%2C19%29%2C%0D%0Atriangle%283.8%2C19%2C-5%2C17%2C-5%2C21%29%2C%0D%0Alocate%284%2C1.2%2C10%29%2Clocate%284%2C6.5%2C17%29%2C%0D%0Alocate%28-4.9%2C20.5%2C2%29%2Clocate%28-1%2C21.2%2C9%29%2C%0D%0Alocate%287.8%2C17%2C12%29%2Clocate%2812.3%2C17%2C5%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Either you are missing some information, or you are expected to say that there are infinte solutions. If you had some other information, like the height, or one angle, you could start by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= half the base<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B7 ALIGN=MIDDLE  ALT=\"x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >= length of the congruent sides,<BR>\n" );
document.write( "and then use that with any extra information<BR>\n" );
document.write( " <BR>\n" );
document.write( "IF it were a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28right%29 ALIGN=MIDDLE  ALT=\"highlight%28right%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > isosceles triangle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C200%2C-1%2C11%2C-1%2C11%2C%0D%0Atriangle%280%2C0%2C10%2C0%2C0%2C10%29%2C%0D%0Arectangle%280%2C0%2C0.5%2C0.5%29%2C%0D%0Alocate%284%2C0%2Cx%2B7%29%2Clocate%280.1%2C5%2Cx%2B7%29%2Clocate%285%2C6%2C2x%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then the base is the hypotenuse, with length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the congruent sides are the legs.<BR>\n" );
document.write( "Then, Pythagoras says<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%5E2%2B%28x%2B7%29%5E2=%282x%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%5E2%2B%28x%2B7%29%5E2=%282x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B7%29%5E2=4x%5E2 ALIGN=MIDDLE  ALT=\"2%28x%2B7%29%5E2=4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2%2B14x%2B49%29=4x%5E2 ALIGN=MIDDLE  ALT=\"2%28x%5E2%2B14x%2B49%29=4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B28x%2B96=4x%5E2 ALIGN=MIDDLE  ALT=\"2x%5E2%2B28x%2B96=4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2x%5E2-28x-96 ALIGN=MIDDLE  ALT=\"0=2x%5E2-28x-96\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Flipping, and dividing both sides by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2x%5E2-28x-96 ALIGN=MIDDLE  ALT=\"0=2x%5E2-28x-96\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-28x-96=0 ALIGN=MIDDLE  ALT=\"2x%5E2-28x-96=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-14x-49=0 ALIGN=MIDDLE  ALT=\"x%5E2-14x-49=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solutions to that equation are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7+%2B-+7sqrt%282%29 ALIGN=MIDDLE  ALT=\"x=7+%2B-+7sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solution with the negative sign is a negative number, which could not be the length of half the base, <BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7+%2B+7sqrt%282%29 ALIGN=MIDDLE  ALT=\"x=7+%2B+7sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B7=+14%2B7sqrt%282%29=about23.9 ALIGN=MIDDLE  ALT=\"x%2B7=+14%2B7sqrt%282%29=about23.9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28rounding%29 ALIGN=MIDDLE  ALT=\"%28rounding%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );