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Answer :
The maximum play area will be achieved when the length of the fence is 100 linear feet.
What is Square feet?
Square feet can be defined as the area of a square with sides of 1 foot.
Square feet for their dogs to play in
This situation can be modeled mathematically as follows:
Let's assume that x is the length of the fence in linear feet and y is the area of the play area in square feet.
Based on the given information, we know that:
y = x * (x - 80) (when x = 100)
y = x * (x - 120) (when x = 80 or 120)
Setting these two equations equal to each other, we can find the value of x that results in the maximum play area:
x * (x - 80) = x * (x - 120)
x^2 - 80x = x^2 - 120x
40x = 40 * 100
x = 100
So, the maximum play area will be achieved when the length of the fence is 100 linear feet. The resulting play area will be 10,000 square feet.
Learn more about square feet here: brainly.com/question/16184973
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