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A rectangular rug has a decorative interior with a 1/2 foot border of uniform width around the outside.
\n" ); document.write( " The length of the decorative area is 3 feet more than the width.
\n" ); document.write( " If the area of the rug (including the border) is 108 ft2, find the dimensions of the rug (including the border).
\n" ); document.write( ":
\n" ); document.write( "let L = the length of the decorated area
\n" ); document.write( "let w = the width
\n" ); document.write( "Also \"length of the decorative area is 3 feet more than the width\"
\n" ); document.write( "L = w+3
\n" ); document.write( ":
\n" ); document.write( "Twice the width of the border (1 ft), is added to the decorated dimensions, therefore
\n" ); document.write( "(L+1)(w+1) = 108
\n" ); document.write( "Replace L with (w+3)
\n" ); document.write( "((w+3)+1)(w+1) = 108
\n" ); document.write( "(w+4)(w+1) = 108
\n" ); document.write( "FOIL
\n" ); document.write( "w^2 + w + 4w + 4 = 108
\n" ); document.write( "w^2 + 5w + 4 - 108 = 0
\n" ); document.write( "w^2 + 5w - 104 = 0
\n" ); document.write( "You can use the quadratic formula, a=1, b=5, c=-104;but this will factor
\n" ); document.write( "(x+13)(x-8) =
\n" ); document.write( "the positive solution is all we want here
\n" ); document.write( "x = 8ft is the width of the decorated area
\n" ); document.write( "then, obviously 11 ft is the length
\n" ); document.write( "Find the overall dimensions, add 1 ft
\n" ); document.write( "12 ft by 9 ft is the overall dimensions of the rug
\n" ); document.write( ":
\n" ); document.write( ";
\n" ); document.write( "Check by finding the area with these dimensions: 12 * 9 = 108
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