SOLUTION: A rectangular playground must have a perimeter of 460 ft and an area of at least 8600 ft. Describe the possible lengths of the playground.

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Question 1168405: A rectangular playground must have a perimeter of 460 ft and an area of at least 8600 ft. Describe the possible lengths of the playground.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
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%28300%2C300%2C-30%2C200%2C-5000%2C9000%2Cx%5E2-230x%2B8600%29