document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158038>Question 158038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A painting canvas has a length 6 inches longer than its width. If the area is 112 in^2, what are the dimensions of the canvas?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116450 by </B><A HREF=/tutors/aboutme.mpl?userid=midwood_trail><B>midwood_trail(310)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=midwood_trail><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=116450\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is not a mixture problem.\r<BR>\n" );
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document.write( "This is a geometry word problem.\r<BR>\n" );
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document.write( "A painting canvas has a length 6 inches longer than its width. If the area is 112 in^2, what are the dimensions of the canvas?\r<BR>\n" );
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document.write( "Let width = x\r<BR>\n" );
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document.write( "Let length = x + 6\r<BR>\n" );
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document.write( "The area given is 112 inches^(2).\r<BR>\n" );
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document.write( "The area of a rectangle (this canvas is a rectangle) is given by the formula<BR>\n" );
document.write( "A = L*W\r<BR>\n" );
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document.write( "We plug and chug.\r<BR>\n" );
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document.write( "112 = (x + 6)(x)\r<BR>\n" );
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document.write( "When I multiply the right side, a quadratic will be the result.\r<BR>\n" );
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document.write( "112 = x^2 + 6x\r<BR>\n" );
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document.write( "Subtract 112 from both sides and equate the entire polynomial to zero.\r<BR>\n" );
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document.write( "x^2 + 6x - 112 = 0\r<BR>\n" );
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document.write( "We now factor the left side of this quadratic equation.\r<BR>\n" );
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document.write( "14 times -8 = -112\r<BR>\n" );
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document.write( "So, the factor becomes (x + 14) (x - 8).\r<BR>\n" );
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document.write( "Set each factor to equal 0 and solve for x.\r<BR>\n" );
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document.write( "x + 14 = 0\r<BR>\n" );
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document.write( "x = -14....This answer for x is REJECTED because length CANNOT be negative.\r<BR>\n" );
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document.write( "x - 8 = 0\r<BR>\n" );
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document.write( "x = 8\r<BR>\n" );
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document.write( "We now know the value of x.\r<BR>\n" );
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document.write( "Since the width = x and I just found the value of x, the width is 8 inches.\r<BR>\n" );
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document.write( "The length = x + 6\r<BR>\n" );
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document.write( "The length = 8 + 6\r<BR>\n" );
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document.write( "The length = 14 inches\r<BR>\n" );
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document.write( "The dimensions of the canvas are:\r<BR>\n" );
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document.write( "width = 8 inches \r<BR>\n" );
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document.write( "length = 14 inches\r<BR>\n" );
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