document.write( "Question 52672This question is from textbook Mathematical Ideas
\n" ); document.write( ": I need help with the dimensions of a strip of flooring around a rug. \r
\n" ); document.write( "\n" ); document.write( "Catarina and Jose want to buy a rug for a room that is 15 feet by 20 feet. They want to leave an even strip of flooring uncovered around the edges of the room. how wide a strip will they have if they buy a rug with an area of 234 square feet? \n" ); document.write( "

Algebra.Com's Answer #35141 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

I need help with the dimensions of \r\n" );
document.write( "a strip of flooring around a rug.  \r\n" );
document.write( "\r\n" );
document.write( "Catarina and Jose want to buy a rug \r\n" );
document.write( "for a room that is 15 feet by 20 feet.  \r\n" );
document.write( "They want to leave an even strip of \r\n" );
document.write( "flooring uncovered around the edges \r\n" );
document.write( "of the room.  how wide a strip will \r\n" );
document.write( "they have if they buy a rug with an \r\n" );
document.write( "area of 234 square feet? \r\n" );
document.write( "\r\n" );
document.write( " _x________________________x_\r\n" );
document.write( "|   |                    |   |x\r\n" );
document.write( "|___|____________________|___| \r\n" );
document.write( "|   |     20-2x          |   |\r\n" );
document.write( "|   |               15-2x|   |\r\n" );
document.write( "|   |                    |   |\r\n" );
document.write( "|___|____________________|___|\r\n" );
document.write( "|x  |                    |   |x\r\n" );
document.write( "|___|____________________|___|\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Area of rug = 234\r\n" );
document.write( "Area of rug = LW = (20-2x)(15-2x)\r\n" );
document.write( "\r\n" );
document.write( "so,\r\n" );
document.write( "\r\n" );
document.write( "(20-2x)(15-2x) = 234\r\n" );
document.write( "\r\n" );
document.write( "Use FOIL:\r\n" );
document.write( "\r\n" );
document.write( "300 - 40x - 30x + 4x² = 234\r\n" );
document.write( "\r\n" );
document.write( "      300 - 70x + 4x² = 234\r\n" );
document.write( "\r\n" );
document.write( "      4x² - 70x + 300 = 234\r\n" );
document.write( "\r\n" );
document.write( "       4x² - 70x + 66 = 0\r\n" );
document.write( "\r\n" );
document.write( "Divide thru by 2\r\n" );
document.write( "\r\n" );
document.write( "       2x² - 35x + 33 = 0\r\n" );
document.write( "\r\n" );
document.write( "     (x - 1)(2x - 33) = 0\r\n" );
document.write( "\r\n" );
document.write( "     x = 1, x = 16.5\r\n" );
document.write( "\r\n" );
document.write( "The larger value is impossible, so the\r\n" );
document.write( "only feasible answer is a 1 foot strip.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );