document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174673>Question 174673</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131339982/algebrahomeworkh>Prentic Hall Mathematics Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> In this problem, they give me the diagram of a rectangle with a diagonal dividing it in two triangles. Each corner is labeled with A, B, C, and D. \r<BR>\n" );
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document.write( "The perimeter of a rectangle is 28 cm. The perimeter of each of the triangles is 24 cm. The diagonal of the rectangle is 2 cm longer than the longer side of the rectangle. <BR>\n" );
document.write( "How do you write a system of three questions in three unknowns?<BR>\n" );
document.write( "How do you simplify the system to a system of two equations in two unknowns?<BR>\n" );
document.write( "And how can I write an augmented matrix for the system?\r<BR>\n" );
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document.write( "This is what I've done so far:<BR>\n" );
document.write( "2a+2b=28<BR>\n" );
document.write( "a+b+x=24<BR>\n" );
document.write( "2+a=?\r<BR>\n" );
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document.write( "Thankyou&Happy New Year!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129715 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=129715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 28 cm. The perimeter of each of the triangles is 24 cm. The diagonal of the rectangle is 2 cm longer than the longer side of the rectangle.<BR>\n" );
document.write( "Let shorter side be a; let longer side be b: let diagonal be c<BR>\n" );
document.write( "Equations:<BR>\n" );
document.write( "2a + 2b = 28<BR>\n" );
document.write( "a + b + c = 24<BR>\n" );
document.write( "c = b + 2<BR>\n" );
document.write( "write a system of three questions in three unknowns<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Rearrange the equations:<BR>\n" );
document.write( "2a   +  2b  +  0  = 28<BR>\n" );
document.write( " a   +   b  +   c = 24<BR>\n" );
document.write( "0    +   b  -   c = -2<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "simplify to a system of two equations in two unknowns?<BR>\n" );
document.write( "let b = c+2<BR>\n" );
document.write( "Then you get:<BR>\n" );
document.write( "2a + 2(c+2) + 0 = 28<BR>\n" );
document.write( "a  + c+2    + c = 24<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "2a + 2c  = 24<BR>\n" );
document.write( " a + 2c  = -2<BR>\n" );
document.write( "----<BR>\n" );
document.write( "write an augmented matrix for the system? <BR>\n" );
document.write( " <BR>\n" );
document.write( "2...2..|..24<BR>\n" );
document.write( "1...2..|..-2<BR>\n" );
document.write( "=====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );