document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187175>Question 1187175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm not really understanding how to set up this factoring equation. The worksheet said to set up each word problem with an equation then solve by factoring and using the zero-product property with no guess and check. The word problem: \r<BR>\n" );
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document.write( "A diagonal of a rectangle is 5 cm longer than 4 times the width of the rectangle. Find the length of the rectangle if it is 1 cm less than the length of the diagonal.\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818110 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A diagonal of a rectangle is 5 cm longer than 4 times the width of the rectangle. Find the length of the rectangle if it is 1 cm less than the length of the diagonal.\r<BR>\n" );
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document.write( "let W equal the width.<BR>\n" );
document.write( "then 4W + 5 equals the diagonal.<BR>\n" );
document.write( "then 4W + 4 equals the length.\r<BR>\n" );
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document.write( "the length and the width and the diagonal form a right triangle.<BR>\n" );
document.write( "4W + 5 is the hypotenuse.<BR>\n" );
document.write( "4W + 4 is one leg.<BR>\n" );
document.write( "W is the other leg.\r<BR>\n" );
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document.write( "since the sum of the square of the legs is equal to the square of the hypotenuse, you get:\r<BR>\n" );
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document.write( "W^2 + (4W+4)^2 = (4W+5)^2\r<BR>\n" );
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document.write( "simplify that equation to get:\r<BR>\n" );
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document.write( "17W^2 + 32W + 16 = 16W^ + 40W + 25\r<BR>\n" );
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document.write( "subtract the right side of the equation from both sides of the equation to get:\r<BR>\n" );
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document.write( "W^2 - 8W - 9 = 0\r<BR>\n" );
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document.write( "that's your quadratic equation.\r<BR>\n" );
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document.write( "factor that to get:\r<BR>\n" );
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document.write( "(W - 9) * (W + 1) = 0\r<BR>\n" );
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document.write( "solve for W to get:\r<BR>\n" );
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document.write( "W = 9 or W = -1\r<BR>\n" );
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document.write( "confirm by replacing W with 9 in the original equation to get:\r<BR>\n" );
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document.write( "4W + 5 = 4 * 9 + 5 = 36 + 5 = 41 is the hypotenuse.<BR>\n" );
document.write( "4W + 4 = 4 * 9 + 4 = 36 + 4 = 40 is the length of the rectangle.<BR>\n" );
document.write( "9 is the width of the rectangle.\r<BR>\n" );
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document.write( "by pythagorus, length^2 + width^2 = diagonal^2.\r<BR>\n" );
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document.write( "you get 40^2 + 9^2 = 41^2.<BR>\n" );
document.write( "this becomes 1681 = 1681, confirming the values of length and width are good.\r<BR>\n" );
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document.write( "your solution is that the length of the rectangle is equal to 40.<BR>\n" );
document.write( "this is one less than the diagonal.\r<BR>\n" );
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document.write( "if there's any part of this you don't understand, then let me know and i'll take you through it.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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