document.write( "Question 886019: Solving a word problem using a quadratic equation with rational roots. if the area of a rectangle is 42ft^2 and the length is 5 feet more than twice the width
\n" ); document.write( "what are the length and width \n" ); document.write( "
Algebra.Com's Answer #535659 by Theo(13342)\"\" \"About 
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x = length
\n" ); document.write( "y = width
\n" ); document.write( "area = x * y
\n" ); document.write( "you get:
\n" ); document.write( "x * y = 42
\n" ); document.write( "since the length is equal to 5 more than 2 times the width, this means that:
\n" ); document.write( "x = 2y + 5
\n" ); document.write( "substitute for x in the equation of x * y = 42 to get:
\n" ); document.write( "(2y + 5) * y = 42
\n" ); document.write( "simplify this to get:
\n" ); document.write( "2y^2 + 5y = 42
\n" ); document.write( "subtract 42 from both sides of this equation to get:
\n" ); document.write( "2y^2 + 5y - 42 = 0
\n" ); document.write( "factor this equation to get:
\n" ); document.write( "(2y-7) * (y+6) = 0
\n" ); document.write( "solve for y to get:
\n" ); document.write( "y = 7/2 or y = -6
\n" ); document.write( "since y can't be negative, then y has to be equal to 7/2.
\n" ); document.write( "since x = 2y + 5, then replace y with 7/2 to get:
\n" ); document.write( "x = 2 * 7/2 + 5 which makes x = 12
\n" ); document.write( "your dimensions are:
\n" ); document.write( "x = 12
\n" ); document.write( "y = 7/2
\n" ); document.write( "multiply x * y and you get 12 * 7/2 = 6 * 7 = 42
\n" ); document.write( "everything checks out so those are your answers.
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