Question 1168405
half-perimeter =230 ft =L+W
so W=230-L
L(230-L)>=8600
-L^2+230L>=8600
or L^2-230L+8600<=0
L=(1/2)(230+/-sqrt(230^2-34400)) sqrt term =136.
L=183, 47.  Between 47 and 183 for length and 230-that number for width. Units feet.
The graph shows the x-values at which the area is greater than 8600 ft^2 (note the unit here). It is the part below 0 because of the inequality above.


{{{graph(300,300,-30,200,-5000,9000,x^2-230x+8600)}}}