document.write( "Question 419217: A farmer has 300 yards of fencing and wants to enclose a rectangular area of 5600 square yards what dimensions should he use? \n" ); document.write( "
Algebra.Com's Answer #293210 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 total amount of fencing is 300 yards, the perimeter of the rectangle must be 300. Perimeter is the sum of all of the sides, that is x + y + x + y. So, we have:\r
\n" ); document.write( "\n" ); document.write( "2x + 2y = 300\r
\n" ); document.write( "\n" ); document.write( "We also know that the area (length times width) is 5600. So we have:\r
\n" ); document.write( "\n" ); document.write( "xy = 5600\r
\n" ); document.write( "\n" ); document.write( "From the first equation, we know that:
\n" ); document.write( "2x + 2y = 300
\n" ); document.write( "x + y = 150 (dividing both sides by 2)
\n" ); document.write( "x = 150 - y (subtracting y from both sides)\r
\n" ); document.write( "\n" ); document.write( "We can make the substitution in the \"area\" equation:
\n" ); document.write( "xy = 5600
\n" ); document.write( "(150 - y)y = 5600 (substituting the expression from above for x)
\n" ); document.write( "150y - y^2 = 5600
\n" ); document.write( "y^2 - 150y + 5600 = 0 (rearranging terms and establishing a quadratic equation)
\n" ); document.write( "(y - 70)(y - 80) = 0 (factoring)
\n" ); document.write( "y = 70 or y = 80\r
\n" ); document.write( "\n" ); document.write( "If y = 70, then x = 80
\n" ); document.write( "If y = 80, then x = 70\r
\n" ); document.write( "\n" ); document.write( "So, the dimension of the fenced in area is 70 by 80.
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