document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120790>Question 120790</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395535921/algebrahomeworkh>Algebra 2 and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> An isosceles riangle has a perimeter of 50 cm.  The sum of the length of the base and the ehight of the triangle is 31 cm.  Find the area of the triangle. \r<BR>\n" );
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document.write( "I set it up for 2a + b = 50<BR>\n" );
document.write( "and b + h = 31\r<BR>\n" );
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document.write( "I have a lot of triangle formulas at my disposal, such as the area of a triangle = 1/2 bh, or Heron's formula for the area of a triangle.  I know that we can also use the special formula for the area of an isosceles triangle.  The quadratic formula of a squared + b squared = c squared too.  But I guess I keep getting stuck with the fact that I've got 3 unknowns rather than 2, re: a, b, and h.  In the other problems in the book, I generally have one linear equation, which I solve for a, then I substitute a into the quadratic equation.  This one has me really stuck.  All help very much appreciated.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88598 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yes, but h is a function of a and b. <BR>\n" );
document.write( "h, a, and b/2 form a right triangle where a is the hypotenuse.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=%28b%2F2%292%2Bh%5E2 ALIGN=MIDDLE  ALT=\"a%5E2=%28b%2F2%292%2Bh%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2=+a%5E2-%28b%2F2%292 ALIGN=MIDDLE  ALT=\"h%5E2=+a%5E2-%28b%2F2%292\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From above, you also know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=31-b ALIGN=MIDDLE  ALT=\"h=31-b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2=+a%5E2-%28b%2F2%292 ALIGN=MIDDLE  ALT=\"h%5E2=+a%5E2-%28b%2F2%292\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2831-b%29%5E2=+a%5E2-%28b%2F2%292 ALIGN=MIDDLE  ALT=\"%2831-b%29%5E2=+a%5E2-%28b%2F2%292\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2Bb=50 ALIGN=MIDDLE  ALT=\"2a%2Bb=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=50-2a ALIGN=MIDDLE  ALT=\"b=50-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2831-50%2B2a%29%5E2=+a%5E2-%2825-a%29%5E2 ALIGN=MIDDLE  ALT=\"%2831-50%2B2a%29%5E2=+a%5E2-%2825-a%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now you have one quadratic equation in a to solve.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282a-19%29%5E2=+a%5E2-%2825-a%29%5E2 ALIGN=MIDDLE  ALT=\"%282a-19%29%5E2=+a%5E2-%2825-a%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=4a%5E2-76a%2B361=a%5E2-%28625-50a%2Ba%5E2%29 ALIGN=MIDDLE  ALT=\"4a%5E2-76a%2B361=a%5E2-%28625-50a%2Ba%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%5E2-76a%2B361=a%5E2-625%2B50a-a%5E2%29 ALIGN=MIDDLE  ALT=\"4a%5E2-76a%2B361=a%5E2-625%2B50a-a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%5E2-76a%2B361=-625%2B50a%29 ALIGN=MIDDLE  ALT=\"4a%5E2-76a%2B361=-625%2B50a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%5E2-126a%2B986=0%29 ALIGN=MIDDLE  ALT=\"4a%5E2-126a%2B986=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28-%28-126%29%2B-sqrt%28%28-126%29%5E2-4%2A4%2A986+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"a=%28-%28-126%29%2B-sqrt%28%28-126%29%5E2-4%2A4%2A986+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28126%2B-sqrt%2815876-15776%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"a=%28126%2B-sqrt%2815876-15776%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28126%2B-sqrt%28100%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"a=%28126%2B-sqrt%28100%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28126%2B-10%29%2F%288%29 ALIGN=MIDDLE  ALT=\"a=%28126%2B-10%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are two solutions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=%28126%2B10%29%2F%288%29 ALIGN=MIDDLE  ALT=\"a%5B1%5D=%28126%2B10%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=%28136%29%2F%288%29 ALIGN=MIDDLE  ALT=\"a%5B1%5D=%28136%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=17 ALIGN=MIDDLE  ALT=\"a%5B1%5D=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=%28126-10%29%2F%288%29 ALIGN=MIDDLE  ALT=\"a%5B2%5D=%28126-10%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=%28116%29%2F%288%29 ALIGN=MIDDLE  ALT=\"a%5B2%5D=%28116%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=14.5 ALIGN=MIDDLE  ALT=\"a%5B2%5D=14.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Placing the values of \"a\" in the original equations, you get,<BR>\n" );
document.write( "a[1]=17<BR>\n" );
document.write( "b[1]=16<BR>\n" );
document.write( "h[1]=15<BR>\n" );
document.write( "Area[1]=120<BR>\n" );
document.write( "a[2]=14.5<BR>\n" );
document.write( "b[2]=21<BR>\n" );
document.write( "h[2]=10<BR>\n" );
document.write( "Area[2]=105 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );