document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158810>Question 158810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a right triangle has hypotenuse with a measure of 20 cm and a perimeter of 47cm. find the measure of the remaining sides. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117017 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=117017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> draw triangle ABC where AB is the height and BC is the hypotenuse and AC is the base.<BR>\n" );
document.write( "A is bottom left, B is top left right above A, C is bottom right.<BR>\n" );
document.write( "let z = BC = 20cm = hypotenuse<BR>\n" );
document.write( "let x = AC = base<BR>\n" );
document.write( "let y = BA = height<BR>\n" );
document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz+=+47 ALIGN=MIDDLE  ALT=\"x%2By%2Bz+=+47\"   DISABLED_style= \"max-width:90%; height:auto;\" > (given)<BR>\n" );
document.write( "this becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2B20+=+47 ALIGN=MIDDLE  ALT=\"x%2By%2B20+=+47\"   DISABLED_style= \"max-width:90%; height:auto;\" > (z is given as 20)<BR>\n" );
document.write( "subtracting 20 from both sides of the equation gets <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=27 ALIGN=MIDDLE  ALT=\"x%2By=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solving for either x or y gets <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=27-x ALIGN=MIDDLE  ALT=\"y=27-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "pythagorean formula states that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+sqrt%28x%5E2+%2B+y%5E2%29 ALIGN=MIDDLE  ALT=\"z+=+sqrt%28x%5E2+%2B+y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+=+sqrt%28x%5E2+%2B+y%5E2%29 ALIGN=MIDDLE  ALT=\"20+=+sqrt%28x%5E2+%2B+y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "squaring both sides of the equation, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400+=+x%5E2+%2B+y%5E2 ALIGN=MIDDLE  ALT=\"400+=+x%5E2+%2B+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (***** this five star equation used below)<BR>\n" );
document.write( "substituting (27-x) for y gets<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400+=+x%5E2+%2B+%2827-x%29%5E2 ALIGN=MIDDLE  ALT=\"400+=+x%5E2+%2B+%2827-x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400+=+x%5E2+%2B+%2827%2A27%29+-54%2Ax+%2B+x%5E2 ALIGN=MIDDLE  ALT=\"400+=+x%5E2+%2B+%2827%2A27%29+-54%2Ax+%2B+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2+-+54%2Ax+%2B+329+=+0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2+-+54%2Ax+%2B+329+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "i could not find any common multiples so i used the quadratic equation to solve.<BR>\n" );
document.write( "the quadratic equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28%28-b%29%2Bsqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x=%28%28-b%29%2Bsqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28%28-b%29-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x=%28%28-b%29-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "in this equation, <BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "b = -54<BR>\n" );
document.write( "c = 329<BR>\n" );
document.write( "after solving the formula (details left out for sake of brevity)<BR>\n" );
document.write( "i got<BR>\n" );
document.write( "x = 17.71307489, and x = 9.286925113<BR>\n" );
document.write( "one of these becomes y, so the answers appear to be<BR>\n" );
document.write( "x = 17.71307489, and y = 9.286925113<BR>\n" );
document.write( "plugging these values into the original equation for x + y + z = 47 yielded 47 = 47 proving the value were good for the perimeter equation.<BR>\n" );
document.write( "results were 17.71307489 + 9.286925113 + 20 = 47 which became 47 = 47.<BR>\n" );
document.write( "plugging these values into the original quadratic equation solving for 400 = 400 = x^2 + y^2(the 5 start equation ***** shown above) yields<BR>\n" );
document.write( "17.713^2 + 9.2819^2 = 400 which became 400 = 400 proving that the values for x and y are good.<BR>\n" );
document.write( "truncated values are shown but full values were used in the calculations.<BR>\n" );
document.write( "answer is<BR>\n" );
document.write( "x = 17.7130<BR>\n" );
document.write( "y = 9.2869<BR>\n" );
document.write( "z = 20<BR>\n" );
document.write( "perimeter = 47 checks out ok<BR>\n" );
document.write( "z^2 = x^2 + y^2 checks out ok<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );