Answer
The length and the with of the garden are $60ft$ and $40ft$
Work Step by Step
Let $x = width$ and $y = length$
Hence the farmer has a rectangular garden plot of $200 ft$ of fencing.
1- The perimeter is
$2(x+y)=200$
$\Rightarrow x+y=100$
Solve for $x$
$x=100-y$
2- The area is
$xy = 2400$
substitute $x=100-y$
$(100-y)y = 2400$
$100y-y^2 = 2400$
$y^2-100y + 2400=0$
$(y-40)(y-60)=0$
$y=40$ or $y=60$
Substitute in $x=100-y$
$x=60$ or $x=40$
The length and the with of the garden are $60ft$ and $40ft$
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