document.write( "Question 313097: A rectangular room has an area of 84 square feet. Its width is 9 more than 3 times the length. What are the dimensions of the rectangle? \n" ); document.write( "
Algebra.Com's Answer #223982 by advedantatutor(4)\"\" \"About 
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Let length = x
\n" ); document.write( "let width = y
\n" ); document.write( "then x x y = 84 -------------- (1)
\n" ); document.write( "But width = 9 more than three times length
\n" ); document.write( "therefore width = 3x + 9
\n" ); document.write( "y = 3x + 9
\n" ); document.write( "Substituting in equation (1) we get
\n" ); document.write( "x x(3x + 9) = 84
\n" ); document.write( "3x^2 + 9x = 84
\n" ); document.write( "3x^2 + 9x -84 = 0
\n" ); document.write( "Solving the quadratic equation above we get
\n" ); document.write( "x =4, x=-7
\n" ); document.write( "Ignoring x = -7 (because length cannot be negative)
\n" ); document.write( "we get x = 4
\n" ); document.write( "then y = 3x + 9 = 12 + 9 = 21.
\n" ); document.write( "Length = 4 feet
\n" ); document.write( "Width = 21 feet.\r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "1) Width = 9 more than 3 times length
\n" ); document.write( "= 3 x length + 9
\n" ); document.write( "= (3 x 4) + 9
\n" ); document.write( "=12 + 9 = 21\r
\n" ); document.write( "\n" ); document.write( "2) Area = Length X Width
\n" ); document.write( "= 4 x 21 = 84 sq. feet.
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