document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033222>Question 1033222</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in triangle ABC, a-b=5 and the area is 50 cm squared. If angle C is 90 degrees, find the side length of c.\r<BR>\n" );
document.write( "\n" );
document.write( "so far, I know that a*b=100 and that a and b are both decimals because no whole numbers that are factors of 100 have a difference of 5.\r<BR>\n" );
document.write( "\n" );
document.write( "**the a is the base of the triangle, b is the height, c is the diagonal and the longest side of the triangle. Also, angle C is a right angle, and angles A and B are located on line c*** </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647826 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=647826\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b=5 ALIGN=MIDDLE  ALT=\"a-b=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b%2B5 ALIGN=MIDDLE  ALT=\"a=b%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ab=100 ALIGN=MIDDLE  ALT=\"a%2Ab=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > , as you said,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2B5%29%2Ab=100 ALIGN=MIDDLE  ALT=\"%28b%2B5%29%2Ab=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2B5b=100 ALIGN=MIDDLE  ALT=\"b%5E2%2B5b=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2B5b-100=0 ALIGN=MIDDLE  ALT=\"b%5E2%2B5b-100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is a quadratic equation.<BR>\n" );
document.write( "When you are lucky, you get a quadratic equation that can be solved by factoring.<BR>\n" );
document.write( "No such luck in this case, because as you said no whole numbers that are factors of 100 have a difference of 5.<BR>\n" );
document.write( "So, we have to solve that equation by completing the square or by using the quadratic formula.<BR>\n" );
document.write( "Either way, the solutions are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%28-5+%2B-+5sqrt%2817%29%29%2F2=%285%2F2%29%28-1+%2B-+Sqrt%2817%29%29 ALIGN=MIDDLE  ALT=\"b=%28-5+%2B-+5sqrt%2817%29%29%2F2=%285%2F2%29%28-1+%2B-+Sqrt%2817%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Since we need a positive <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=%28-5+%2B+5sqrt%2817%29%29%2F2=%285%2F2%29%28-1+%2B+sqrt%2817%29%29%29 ALIGN=MIDDLE  ALT=\"highlight%28b=%28-5+%2B+5sqrt%2817%29%29%2F2=%285%2F2%29%28-1+%2B+sqrt%2817%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=5%2B%28-5+%2B+5sqrt%2817%29%29%2F2=%285+%2B+5sqrt%2817%29%29%2F2=%285%2F2%29%281+%2B+sqrt%2817%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Accrording to the Pythagorean theorem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=%28%285%2F2%29%28sqrt%2817%29%2B1%29%29%5E2%2B%28%285%2F2%29%28sqrt%2817%29-1%29%29%5E2=%285%2F2%29%5E2%28sqrt%2817%29%2B1%29%5E2%2B%285%2F2%29%5E2%28sqrt%2817%29-1%29%5E2=%285%2F2%29%5E2%2817%2B2sqrt%2817%29%2B1%2B17-2sqrt%2817%29%2B1%29=%285%2F2%29%5E2%2A36=%285%2F2%29%5E2%2A6%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28%285%2F2%29%5E2%2A6%5E2%29=%285%2F2%29%2A6=highlight%2815%29 ALIGN=MIDDLE  ALT=\"c=sqrt%28%285%2F2%29%5E2%2A6%5E2%29=%285%2F2%29%2A6=highlight%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the hypotenuse of the right triangle) measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2815cm%29 ALIGN=MIDDLE  ALT=\"highlight%2815cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );