document.write( "Question 418780: the area of a rectangle is 56 square feet. its lenght is 10 feet longer than the width. find the lenght and width? \n" ); document.write( "
Algebra.Com's Answer #293008 by duckness73(47)\"\" \"About 
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Let x = width of the rectangle
\n" ); document.write( "Let y = length of the rectangle\r
\n" ); document.write( "\n" ); document.write( "Since the area of a rectangle is the width * length, and we know that this rectangle has an area of 56 square feet:
\n" ); document.write( "x * y = 56\r
\n" ); document.write( "\n" ); document.write( "Since the length of the rectangle is 10 feet longer than the width:
\n" ); document.write( "y = x + 10\r
\n" ); document.write( "\n" ); document.write( "Using the area equation from above, we have:
\n" ); document.write( "x * (x + 10) = 56 which can be simplified as:\r
\n" ); document.write( "\n" ); document.write( "x**2 + 10x = 56
\n" ); document.write( "x**2 + 10x - 56 = 0 which is a quadratic equation.\r
\n" ); document.write( "\n" ); document.write( "Using factoring to solve this equation, we have:
\n" ); document.write( "(x + 14)(x - 4) = 0 which means that
\n" ); document.write( "x = -14 or x = 4. So the width of the rectangle is either -14 or 4 feet.\r
\n" ); document.write( "\n" ); document.write( "So, which is it? Since it doesn't make any sense to have a rectangle with a negative width, the width of a rectangle cannot be -14 feet, so the width must be 4. Since the length (which is y) is 10 feet longer than the width, we have
\n" ); document.write( "y = x + 10 = 4 + 10 = 14\r
\n" ); document.write( "\n" ); document.write( "So, the length (y) of the rectangle is 14 and the width (x) is 4.
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