document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=238378>Question 238378</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,<BR>\n" );
document.write( "Can you please help me with this problem?<BR>\n" );
document.write( "Find the dimensions of a rectangle whose perimeter is 46m and whose area is 126m.<BR>\n" );
document.write( " Also<BR>\n" );
document.write( "The length of a rectangle is 8 cm greater then its width. Find the dimensions if its area is 105 cm<BR>\n" );
document.write( "We need to solve it using quadratics and possibly using factoring! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175339 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=175339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the dimensions of a rectangle whose perimeter is 46m and whose area is 126m.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The perimeter equation:<BR>\n" );
document.write( "2L + 2W = 126<BR>\n" );
document.write( "Simplify divide by 2<BR>\n" );
document.write( "L + W = 23<BR>\n" );
document.write( "W = (23-L); use for substitution<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The area<BR>\n" );
document.write( "L * W = 126<BR>\n" );
document.write( "Substitute (23-L) for W<BR>\n" );
document.write( "L*(23-L) = 126<BR>\n" );
document.write( "23L - L^2 = 126<BR>\n" );
document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "-L^2 + 23L - 126 = 0<BR>\n" );
document.write( "Multiply by -1, easier to factor:<BR>\n" );
document.write( "L^2 - 23L + 126 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(L-9)(L-14) = 0<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "L = 9, then W = 14<BR>\n" );
document.write( "or<BR>\n" );
document.write( "L = 14. then W = 9<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check: 2(14)+2(9) = 46<BR>\n" );
document.write( "and area: 14 * 9 = 126<BR>\n" );
document.write( ":<BR>\n" );
document.write( ";<BR>\n" );
document.write( "The length of a rectangle is 8 cm greater then its width. Find the dimensions if its area is 105 cm<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = the width<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+8) = the length<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Area<BR>\n" );
document.write( "x(x+8) = 105<BR>\n" );
document.write( "x^2 + 8x - 105 = 0; our old friend, the quadratic equation!<BR>\n" );
document.write( "factors to<BR>\n" );
document.write( "(x+15)(x-7) = 0<BR>\n" );
document.write( "The positive solution is what we want here<BR>\n" );
document.write( "x = 7 cm, the width<BR>\n" );
document.write( "then<BR>\n" );
document.write( "7 + 8 = 15 cm; the length<BR>\n" );
document.write( ";<BR>\n" );
document.write( "It this true?: 7 * 15 = 105 sq cm<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );